- FindStat

edit this statistic or download as text // json

Identifier

St001293: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,2]=>9
[2,1]=>8
[1,2,3]=>55
[1,3,2]=>54
[2,1,3]=>50
[2,3,1]=>47
[3,1,2]=>47
[3,2,1]=>45
[1,2,3,4]=>875
[1,2,4,3]=>870
[1,3,2,4]=>861
[1,3,4,2]=>848
[1,4,2,3]=>848
[1,4,3,2]=>840
[2,1,3,4]=>805
[2,1,4,3]=>800
[2,3,1,4]=>763
[2,3,4,1]=>736
[2,4,1,3]=>750
[2,4,3,1]=>728
[3,1,2,4]=>763
[3,1,4,2]=>750
[3,2,1,4]=>735
[3,2,4,1]=>708
[3,4,1,2]=>700
[3,4,2,1]=>686
[4,1,2,3]=>736
[4,1,3,2]=>728
[4,2,1,3]=>708
[4,2,3,1]=>686
[4,3,1,2]=>686
[4,3,2,1]=>672
[1,2,3,4,5]=>2877
[1,2,3,5,4]=>2870
[1,2,4,3,5]=>2862
[1,2,4,5,3]=>2845
[1,2,5,3,4]=>2845
[1,2,5,4,3]=>2835
[1,3,2,4,5]=>2835
[1,3,2,5,4]=>2828
[1,3,4,2,5]=>2796
[1,3,4,5,2]=>2764
[1,3,5,2,4]=>2779
[1,3,5,4,2]=>2754
[1,4,2,3,5]=>2796
[1,4,2,5,3]=>2779
[1,4,3,2,5]=>2772
[1,4,3,5,2]=>2740
[1,4,5,2,3]=>2730
[1,4,5,3,2]=>2715
[1,5,2,3,4]=>2764
[1,5,2,4,3]=>2754
[1,5,3,2,4]=>2740
[1,5,3,4,2]=>2715
[1,5,4,2,3]=>2715
[1,5,4,3,2]=>2700
[2,1,3,4,5]=>2667
[2,1,3,5,4]=>2660
[2,1,4,3,5]=>2652
[2,1,4,5,3]=>2635
[2,1,5,3,4]=>2635
[2,1,5,4,3]=>2625
[2,3,1,4,5]=>2541
[2,3,1,5,4]=>2534
[2,3,4,1,5]=>2460
[2,3,4,5,1]=>2404
[2,3,5,1,4]=>2443
[2,3,5,4,1]=>2394
[2,4,1,3,5]=>2502
[2,4,1,5,3]=>2485
[2,4,3,1,5]=>2436
[2,4,3,5,1]=>2380
[2,4,5,1,3]=>2394
[2,4,5,3,1]=>2355
[2,5,1,3,4]=>2470
[2,5,1,4,3]=>2460
[2,5,3,1,4]=>2404
[2,5,3,4,1]=>2355
[2,5,4,1,3]=>2379
[2,5,4,3,1]=>2340
[3,1,2,4,5]=>2541
[3,1,2,5,4]=>2534
[3,1,4,2,5]=>2502
[3,1,4,5,2]=>2470
[3,1,5,2,4]=>2485
[3,1,5,4,2]=>2460
[3,2,1,4,5]=>2457
[3,2,1,5,4]=>2450
[3,2,4,1,5]=>2376
[3,2,4,5,1]=>2320
[3,2,5,1,4]=>2359
[3,2,5,4,1]=>2310
[3,4,1,2,5]=>2352
[3,4,1,5,2]=>2320
[3,4,2,1,5]=>2310
[3,4,2,5,1]=>2254
[3,4,5,1,2]=>2229
[3,4,5,2,1]=>2205
[3,5,1,2,4]=>2320
[3,5,1,4,2]=>2295
[3,5,2,1,4]=>2278
[3,5,2,4,1]=>2229
[3,5,4,1,2]=>2214
[3,5,4,2,1]=>2190
[4,1,2,3,5]=>2460
[4,1,2,5,3]=>2443
[4,1,3,2,5]=>2436
[4,1,3,5,2]=>2404
[4,1,5,2,3]=>2394
[4,1,5,3,2]=>2379
[4,2,1,3,5]=>2376
[4,2,1,5,3]=>2359
[4,2,3,1,5]=>2310
[4,2,3,5,1]=>2254
[4,2,5,1,3]=>2268
[4,2,5,3,1]=>2229
[4,3,1,2,5]=>2310
[4,3,1,5,2]=>2278
[4,3,2,1,5]=>2268
[4,3,2,5,1]=>2212
[4,3,5,1,2]=>2187
[4,3,5,2,1]=>2163
[4,5,1,2,3]=>2229
[4,5,1,3,2]=>2214
[4,5,2,1,3]=>2187
[4,5,2,3,1]=>2148
[4,5,3,1,2]=>2148
[4,5,3,2,1]=>2124
[5,1,2,3,4]=>2404
[5,1,2,4,3]=>2394
[5,1,3,2,4]=>2380
[5,1,3,4,2]=>2355
[5,1,4,2,3]=>2355
[5,1,4,3,2]=>2340
[5,2,1,3,4]=>2320
[5,2,1,4,3]=>2310
[5,2,3,1,4]=>2254
[5,2,3,4,1]=>2205
[5,2,4,1,3]=>2229
[5,2,4,3,1]=>2190
[5,3,1,2,4]=>2254
[5,3,1,4,2]=>2229
[5,3,2,1,4]=>2212
[5,3,2,4,1]=>2163
[5,3,4,1,2]=>2148
[5,3,4,2,1]=>2124
[5,4,1,2,3]=>2205
[5,4,1,3,2]=>2190
[5,4,2,1,3]=>2163
[5,4,2,3,1]=>2124
[5,4,3,1,2]=>2124
[5,4,3,2,1]=>2100
[1,2,3,4,5,6]=>33957
[1,2,3,4,6,5]=>33915
[1,2,3,5,4,6]=>33880
[1,2,3,5,6,4]=>33782
[1,2,3,6,4,5]=>33782
[1,2,3,6,5,4]=>33726
[1,2,4,3,5,6]=>33792
[1,2,4,3,6,5]=>33750
[1,2,4,5,3,6]=>33605
[1,2,4,5,6,3]=>33430
[1,2,4,6,3,5]=>33507
[1,2,4,6,5,3]=>33374
[1,2,5,3,4,6]=>33605
[1,2,5,3,6,4]=>33507
[1,2,5,4,3,6]=>33495
[1,2,5,4,6,3]=>33320
[1,2,5,6,3,4]=>33264
[1,2,5,6,4,3]=>33187
[1,2,6,3,4,5]=>33430
[1,2,6,3,5,4]=>33374
[1,2,6,4,3,5]=>33320
[1,2,6,4,5,3]=>33187
[1,2,6,5,3,4]=>33187
[1,2,6,5,4,3]=>33110
[1,3,2,4,5,6]=>33495
[1,3,2,4,6,5]=>33453
[1,3,2,5,4,6]=>33418
[1,3,2,5,6,4]=>33320
[1,3,2,6,4,5]=>33320
[1,3,2,6,5,4]=>33264
[1,3,4,2,5,6]=>33066
[1,3,4,2,6,5]=>33024
[1,3,4,5,2,6]=>32714
[1,3,4,5,6,2]=>32429
[1,3,4,6,2,5]=>32616
[1,3,4,6,5,2]=>32373
[1,3,5,2,4,6]=>32879
[1,3,5,2,6,4]=>32781
[1,3,5,4,2,6]=>32604
[1,3,5,4,6,2]=>32319
[1,3,5,6,2,4]=>32373
[1,3,5,6,4,2]=>32186
[1,3,6,2,4,5]=>32704
[1,3,6,2,5,4]=>32648
[1,3,6,4,2,5]=>32429
[1,3,6,4,5,2]=>32186
[1,3,6,5,2,4]=>32296
[1,3,6,5,4,2]=>32109
[1,4,2,3,5,6]=>33066
[1,4,2,3,6,5]=>33024
[1,4,2,5,3,6]=>32879
[1,4,2,5,6,3]=>32704
[1,4,2,6,3,5]=>32781
[1,4,2,6,5,3]=>32648
[1,4,3,2,5,6]=>32802
[1,4,3,2,6,5]=>32760
[1,4,3,5,2,6]=>32450
[1,4,3,5,6,2]=>32165
[1,4,3,6,2,5]=>32352
[1,4,3,6,5,2]=>32109
[1,4,5,2,3,6]=>32340
[1,4,5,2,6,3]=>32165
[1,4,5,3,2,6]=>32175
[1,4,5,3,6,2]=>31890
[1,4,5,6,2,3]=>31757
[1,4,5,6,3,2]=>31647
[1,4,6,2,3,5]=>32165
[1,4,6,2,5,3]=>32032
[1,4,6,3,2,5]=>32000
[1,4,6,3,5,2]=>31757
[1,4,6,5,2,3]=>31680
[1,4,6,5,3,2]=>31570
[1,5,2,3,4,6]=>32714
[1,5,2,3,6,4]=>32616
[1,5,2,4,3,6]=>32604
[1,5,2,4,6,3]=>32429
[1,5,2,6,3,4]=>32373
[1,5,2,6,4,3]=>32296
[1,5,3,2,4,6]=>32450
[1,5,3,2,6,4]=>32352
[1,5,3,4,2,6]=>32175
[1,5,3,4,6,2]=>31890
[1,5,3,6,2,4]=>31944
[1,5,3,6,4,2]=>31757
[1,5,4,2,3,6]=>32175
[1,5,4,2,6,3]=>32000
[1,5,4,3,2,6]=>32010
[1,5,4,3,6,2]=>31725
[1,5,4,6,2,3]=>31592
[1,5,4,6,3,2]=>31482
[1,5,6,2,3,4]=>31757
[1,5,6,2,4,3]=>31680
[1,5,6,3,2,4]=>31592
[1,5,6,3,4,2]=>31405
[1,5,6,4,2,3]=>31405
[1,5,6,4,3,2]=>31295
[1,6,2,3,4,5]=>32429
[1,6,2,3,5,4]=>32373
[1,6,2,4,3,5]=>32319
[1,6,2,4,5,3]=>32186
[1,6,2,5,3,4]=>32186
[1,6,2,5,4,3]=>32109
[1,6,3,2,4,5]=>32165
[1,6,3,2,5,4]=>32109
[1,6,3,4,2,5]=>31890
[1,6,3,4,5,2]=>31647
[1,6,3,5,2,4]=>31757
[1,6,3,5,4,2]=>31570
[1,6,4,2,3,5]=>31890
[1,6,4,2,5,3]=>31757
[1,6,4,3,2,5]=>31725
[1,6,4,3,5,2]=>31482
[1,6,4,5,2,3]=>31405
[1,6,4,5,3,2]=>31295
[1,6,5,2,3,4]=>31647
[1,6,5,2,4,3]=>31570
[1,6,5,3,2,4]=>31482
[1,6,5,3,4,2]=>31295
[1,6,5,4,2,3]=>31295
[1,6,5,4,3,2]=>31185
[2,1,3,4,5,6]=>31647
[2,1,3,4,6,5]=>31605
[2,1,3,5,4,6]=>31570
[2,1,3,5,6,4]=>31472
[2,1,3,6,4,5]=>31472
[2,1,3,6,5,4]=>31416
[2,1,4,3,5,6]=>31482
[2,1,4,3,6,5]=>31440
[2,1,4,5,3,6]=>31295
[2,1,4,5,6,3]=>31120
[2,1,4,6,3,5]=>31197
[2,1,4,6,5,3]=>31064
[2,1,5,3,4,6]=>31295
[2,1,5,3,6,4]=>31197
[2,1,5,4,3,6]=>31185
[2,1,5,4,6,3]=>31010
[2,1,5,6,3,4]=>30954
[2,1,5,6,4,3]=>30877
[2,1,6,3,4,5]=>31120
[2,1,6,3,5,4]=>31064
[2,1,6,4,3,5]=>31010
[2,1,6,4,5,3]=>30877
[2,1,6,5,3,4]=>30877
[2,1,6,5,4,3]=>30800
[2,3,1,4,5,6]=>30261
[2,3,1,4,6,5]=>30219
[2,3,1,5,4,6]=>30184
[2,3,1,5,6,4]=>30086
[2,3,1,6,4,5]=>30086
[2,3,1,6,5,4]=>30030
[2,3,4,1,5,6]=>29370
[2,3,4,1,6,5]=>29328
[2,3,4,5,1,6]=>28754
[2,3,4,5,6,1]=>28304
[2,3,4,6,1,5]=>28656
[2,3,4,6,5,1]=>28248
[2,3,5,1,4,6]=>29183
[2,3,5,1,6,4]=>29085
[2,3,5,4,1,6]=>28644
[2,3,5,4,6,1]=>28194
[2,3,5,6,1,4]=>28413
[2,3,5,6,4,1]=>28061
[2,3,6,1,4,5]=>29008
[2,3,6,1,5,4]=>28952
[2,3,6,4,1,5]=>28469
[2,3,6,4,5,1]=>28061
[2,3,6,5,1,4]=>28336
[2,3,6,5,4,1]=>27984
[2,4,1,3,5,6]=>29832
[2,4,1,3,6,5]=>29790
[2,4,1,5,3,6]=>29645
[2,4,1,5,6,3]=>29470
[2,4,1,6,3,5]=>29547
[2,4,1,6,5,3]=>29414
[2,4,3,1,5,6]=>29106
[2,4,3,1,6,5]=>29064
[2,4,3,5,1,6]=>28490
[2,4,3,5,6,1]=>28040
[2,4,3,6,1,5]=>28392
[2,4,3,6,5,1]=>27984
[2,4,5,1,3,6]=>28644
[2,4,5,1,6,3]=>28469
[2,4,5,3,1,6]=>28215
[2,4,5,3,6,1]=>27765
[2,4,5,6,1,3]=>27797
[2,4,5,6,3,1]=>27522
[2,4,6,1,3,5]=>28469
[2,4,6,1,5,3]=>28336
[2,4,6,3,1,5]=>28040
[2,4,6,3,5,1]=>27632
[2,4,6,5,1,3]=>27720
[2,4,6,5,3,1]=>27445
[2,5,1,3,4,6]=>29480
[2,5,1,3,6,4]=>29382
[2,5,1,4,3,6]=>29370
[2,5,1,4,6,3]=>29195
[2,5,1,6,3,4]=>29139
[2,5,1,6,4,3]=>29062
[2,5,3,1,4,6]=>28754
[2,5,3,1,6,4]=>28656
[2,5,3,4,1,6]=>28215
[2,5,3,4,6,1]=>27765
[2,5,3,6,1,4]=>27984
[2,5,3,6,4,1]=>27632
[2,5,4,1,3,6]=>28479
[2,5,4,1,6,3]=>28304
[2,5,4,3,1,6]=>28050
[2,5,4,3,6,1]=>27600
[2,5,4,6,1,3]=>27632
[2,5,4,6,3,1]=>27357
[2,5,6,1,3,4]=>28061
[2,5,6,1,4,3]=>27984
[2,5,6,3,1,4]=>27632
[2,5,6,3,4,1]=>27280
[2,5,6,4,1,3]=>27445
[2,5,6,4,3,1]=>27170
[2,6,1,3,4,5]=>29195
[2,6,1,3,5,4]=>29139
[2,6,1,4,3,5]=>29085
[2,6,1,4,5,3]=>28952
[2,6,1,5,3,4]=>28952
[2,6,1,5,4,3]=>28875
[2,6,3,1,4,5]=>28469
[2,6,3,1,5,4]=>28413
[2,6,3,4,1,5]=>27930
[2,6,3,4,5,1]=>27522
[2,6,3,5,1,4]=>27797
[2,6,3,5,4,1]=>27445
[2,6,4,1,3,5]=>28194
[2,6,4,1,5,3]=>28061
[2,6,4,3,1,5]=>27765
[2,6,4,3,5,1]=>27357
[2,6,4,5,1,3]=>27445
[2,6,4,5,3,1]=>27170
[2,6,5,1,3,4]=>27951
[2,6,5,1,4,3]=>27874
[2,6,5,3,1,4]=>27522
[2,6,5,3,4,1]=>27170
[2,6,5,4,1,3]=>27335
[2,6,5,4,3,1]=>27060
[3,1,2,4,5,6]=>30261
[3,1,2,4,6,5]=>30219
[3,1,2,5,4,6]=>30184
[3,1,2,5,6,4]=>30086
[3,1,2,6,4,5]=>30086
[3,1,2,6,5,4]=>30030
[3,1,4,2,5,6]=>29832
[3,1,4,2,6,5]=>29790
[3,1,4,5,2,6]=>29480
[3,1,4,5,6,2]=>29195
[3,1,4,6,2,5]=>29382
[3,1,4,6,5,2]=>29139
[3,1,5,2,4,6]=>29645
[3,1,5,2,6,4]=>29547
[3,1,5,4,2,6]=>29370
[3,1,5,4,6,2]=>29085
[3,1,5,6,2,4]=>29139
[3,1,5,6,4,2]=>28952
[3,1,6,2,4,5]=>29470
[3,1,6,2,5,4]=>29414
[3,1,6,4,2,5]=>29195
[3,1,6,4,5,2]=>28952
[3,1,6,5,2,4]=>29062
[3,1,6,5,4,2]=>28875
[3,2,1,4,5,6]=>29337
[3,2,1,4,6,5]=>29295
[3,2,1,5,4,6]=>29260
[3,2,1,5,6,4]=>29162
[3,2,1,6,4,5]=>29162
[3,2,1,6,5,4]=>29106
[3,2,4,1,5,6]=>28446
[3,2,4,1,6,5]=>28404
[3,2,4,5,1,6]=>27830
[3,2,4,5,6,1]=>27380
[3,2,4,6,1,5]=>27732
[3,2,4,6,5,1]=>27324
[3,2,5,1,4,6]=>28259
[3,2,5,1,6,4]=>28161
[3,2,5,4,1,6]=>27720
[3,2,5,4,6,1]=>27270
[3,2,5,6,1,4]=>27489
[3,2,5,6,4,1]=>27137
[3,2,6,1,4,5]=>28084
[3,2,6,1,5,4]=>28028
[3,2,6,4,1,5]=>27545
[3,2,6,4,5,1]=>27137
[3,2,6,5,1,4]=>27412
[3,2,6,5,4,1]=>27060
[3,4,1,2,5,6]=>28182
[3,4,1,2,6,5]=>28140
[3,4,1,5,2,6]=>27830
[3,4,1,5,6,2]=>27545
[3,4,1,6,2,5]=>27732
[3,4,1,6,5,2]=>27489
[3,4,2,1,5,6]=>27720
[3,4,2,1,6,5]=>27678
[3,4,2,5,1,6]=>27104
[3,4,2,5,6,1]=>26654
[3,4,2,6,1,5]=>27006
[3,4,2,6,5,1]=>26598
[3,4,5,1,2,6]=>26829
[3,4,5,1,6,2]=>26544
[3,4,5,2,1,6]=>26565
[3,4,5,2,6,1]=>26115
[3,4,5,6,1,2]=>25872
[3,4,5,6,2,1]=>25707
[3,4,6,1,2,5]=>26654
[3,4,6,1,5,2]=>26411
[3,4,6,2,1,5]=>26390
[3,4,6,2,5,1]=>25982
[3,4,6,5,1,2]=>25795
[3,4,6,5,2,1]=>25630
[3,5,1,2,4,6]=>27830
[3,5,1,2,6,4]=>27732
[3,5,1,4,2,6]=>27555
[3,5,1,4,6,2]=>27270
[3,5,1,6,2,4]=>27324
[3,5,1,6,4,2]=>27137
[3,5,2,1,4,6]=>27368
[3,5,2,1,6,4]=>27270
[3,5,2,4,1,6]=>26829
[3,5,2,4,6,1]=>26379
[3,5,2,6,1,4]=>26598
[3,5,2,6,4,1]=>26246
[3,5,4,1,2,6]=>26664
[3,5,4,1,6,2]=>26379
[3,5,4,2,1,6]=>26400
[3,5,4,2,6,1]=>25950
[3,5,4,6,1,2]=>25707
[3,5,4,6,2,1]=>25542
[3,5,6,1,2,4]=>26246
[3,5,6,1,4,2]=>26059
[3,5,6,2,1,4]=>25982
[3,5,6,2,4,1]=>25630
[3,5,6,4,1,2]=>25520
[3,5,6,4,2,1]=>25355
[3,6,1,2,4,5]=>27545
[3,6,1,2,5,4]=>27489
[3,6,1,4,2,5]=>27270
[3,6,1,4,5,2]=>27027
[3,6,1,5,2,4]=>27137
[3,6,1,5,4,2]=>26950
[3,6,2,1,4,5]=>27083
[3,6,2,1,5,4]=>27027
[3,6,2,4,1,5]=>26544
[3,6,2,4,5,1]=>26136
[3,6,2,5,1,4]=>26411
[3,6,2,5,4,1]=>26059
[3,6,4,1,2,5]=>26379
[3,6,4,1,5,2]=>26136
[3,6,4,2,1,5]=>26115
[3,6,4,2,5,1]=>25707
[3,6,4,5,1,2]=>25520
[3,6,4,5,2,1]=>25355
[3,6,5,1,2,4]=>26136
[3,6,5,1,4,2]=>25949
[3,6,5,2,1,4]=>25872
[3,6,5,2,4,1]=>25520
[3,6,5,4,1,2]=>25410
[3,6,5,4,2,1]=>25245
[4,1,2,3,5,6]=>29370
[4,1,2,3,6,5]=>29328
[4,1,2,5,3,6]=>29183
[4,1,2,5,6,3]=>29008
[4,1,2,6,3,5]=>29085
[4,1,2,6,5,3]=>28952
[4,1,3,2,5,6]=>29106
[4,1,3,2,6,5]=>29064
[4,1,3,5,2,6]=>28754
[4,1,3,5,6,2]=>28469
[4,1,3,6,2,5]=>28656
[4,1,3,6,5,2]=>28413
[4,1,5,2,3,6]=>28644
[4,1,5,2,6,3]=>28469
[4,1,5,3,2,6]=>28479
[4,1,5,3,6,2]=>28194
[4,1,5,6,2,3]=>28061
[4,1,5,6,3,2]=>27951
[4,1,6,2,3,5]=>28469
[4,1,6,2,5,3]=>28336
[4,1,6,3,2,5]=>28304
[4,1,6,3,5,2]=>28061
[4,1,6,5,2,3]=>27984
[4,1,6,5,3,2]=>27874
[4,2,1,3,5,6]=>28446
[4,2,1,3,6,5]=>28404
[4,2,1,5,3,6]=>28259
[4,2,1,5,6,3]=>28084
[4,2,1,6,3,5]=>28161
[4,2,1,6,5,3]=>28028
[4,2,3,1,5,6]=>27720
[4,2,3,1,6,5]=>27678
[4,2,3,5,1,6]=>27104
[4,2,3,5,6,1]=>26654
[4,2,3,6,1,5]=>27006
[4,2,3,6,5,1]=>26598
[4,2,5,1,3,6]=>27258
[4,2,5,1,6,3]=>27083
[4,2,5,3,1,6]=>26829
[4,2,5,3,6,1]=>26379
[4,2,5,6,1,3]=>26411
[4,2,5,6,3,1]=>26136
[4,2,6,1,3,5]=>27083
[4,2,6,1,5,3]=>26950
[4,2,6,3,1,5]=>26654
[4,2,6,3,5,1]=>26246
[4,2,6,5,1,3]=>26334
[4,2,6,5,3,1]=>26059
[4,3,1,2,5,6]=>27720
[4,3,1,2,6,5]=>27678
[4,3,1,5,2,6]=>27368
[4,3,1,5,6,2]=>27083
[4,3,1,6,2,5]=>27270
[4,3,1,6,5,2]=>27027
[4,3,2,1,5,6]=>27258
[4,3,2,1,6,5]=>27216
[4,3,2,5,1,6]=>26642
[4,3,2,5,6,1]=>26192
[4,3,2,6,1,5]=>26544
[4,3,2,6,5,1]=>26136
[4,3,5,1,2,6]=>26367
[4,3,5,1,6,2]=>26082
[4,3,5,2,1,6]=>26103
[4,3,5,2,6,1]=>25653
[4,3,5,6,1,2]=>25410
[4,3,5,6,2,1]=>25245
[4,3,6,1,2,5]=>26192
[4,3,6,1,5,2]=>25949
[4,3,6,2,1,5]=>25928
[4,3,6,2,5,1]=>25520
[4,3,6,5,1,2]=>25333
[4,3,6,5,2,1]=>25168
[4,5,1,2,3,6]=>26829
[4,5,1,2,6,3]=>26654
[4,5,1,3,2,6]=>26664
[4,5,1,3,6,2]=>26379
[4,5,1,6,2,3]=>26246
[4,5,1,6,3,2]=>26136
[4,5,2,1,3,6]=>26367
[4,5,2,1,6,3]=>26192
[4,5,2,3,1,6]=>25938
[4,5,2,3,6,1]=>25488
[4,5,2,6,1,3]=>25520
[4,5,2,6,3,1]=>25245
[4,5,3,1,2,6]=>25938
[4,5,3,1,6,2]=>25653
[4,5,3,2,1,6]=>25674
[4,5,3,2,6,1]=>25224
[4,5,3,6,1,2]=>24981
[4,5,3,6,2,1]=>24816
[4,5,6,1,2,3]=>25168
[4,5,6,1,3,2]=>25058
[4,5,6,2,1,3]=>24904
[4,5,6,2,3,1]=>24629
[4,5,6,3,1,2]=>24629
[4,5,6,3,2,1]=>24464
[4,6,1,2,3,5]=>26544
[4,6,1,2,5,3]=>26411
[4,6,1,3,2,5]=>26379
[4,6,1,3,5,2]=>26136
[4,6,1,5,2,3]=>26059
[4,6,1,5,3,2]=>25949
[4,6,2,1,3,5]=>26082
[4,6,2,1,5,3]=>25949
[4,6,2,3,1,5]=>25653
[4,6,2,3,5,1]=>25245
[4,6,2,5,1,3]=>25333
[4,6,2,5,3,1]=>25058
[4,6,3,1,2,5]=>25653
[4,6,3,1,5,2]=>25410
[4,6,3,2,1,5]=>25389
[4,6,3,2,5,1]=>24981
[4,6,3,5,1,2]=>24794
[4,6,3,5,2,1]=>24629
[4,6,5,1,2,3]=>25058
[4,6,5,1,3,2]=>24948
[4,6,5,2,1,3]=>24794
[4,6,5,2,3,1]=>24519
[4,6,5,3,1,2]=>24519
[4,6,5,3,2,1]=>24354
[5,1,2,3,4,6]=>28754
[5,1,2,3,6,4]=>28656
[5,1,2,4,3,6]=>28644
[5,1,2,4,6,3]=>28469
[5,1,2,6,3,4]=>28413
[5,1,2,6,4,3]=>28336
[5,1,3,2,4,6]=>28490
[5,1,3,2,6,4]=>28392
[5,1,3,4,2,6]=>28215
[5,1,3,4,6,2]=>27930
[5,1,3,6,2,4]=>27984
[5,1,3,6,4,2]=>27797
[5,1,4,2,3,6]=>28215
[5,1,4,2,6,3]=>28040
[5,1,4,3,2,6]=>28050
[5,1,4,3,6,2]=>27765
[5,1,4,6,2,3]=>27632
[5,1,4,6,3,2]=>27522
[5,1,6,2,3,4]=>27797
[5,1,6,2,4,3]=>27720
[5,1,6,3,2,4]=>27632
[5,1,6,3,4,2]=>27445
[5,1,6,4,2,3]=>27445
[5,1,6,4,3,2]=>27335
[5,2,1,3,4,6]=>27830
[5,2,1,3,6,4]=>27732
[5,2,1,4,3,6]=>27720
[5,2,1,4,6,3]=>27545
[5,2,1,6,3,4]=>27489
[5,2,1,6,4,3]=>27412
[5,2,3,1,4,6]=>27104
[5,2,3,1,6,4]=>27006
[5,2,3,4,1,6]=>26565
[5,2,3,4,6,1]=>26115
[5,2,3,6,1,4]=>26334
[5,2,3,6,4,1]=>25982
[5,2,4,1,3,6]=>26829
[5,2,4,1,6,3]=>26654
[5,2,4,3,1,6]=>26400
[5,2,4,3,6,1]=>25950
[5,2,4,6,1,3]=>25982
[5,2,4,6,3,1]=>25707
[5,2,6,1,3,4]=>26411
[5,2,6,1,4,3]=>26334
[5,2,6,3,1,4]=>25982
[5,2,6,3,4,1]=>25630
[5,2,6,4,1,3]=>25795
[5,2,6,4,3,1]=>25520
[5,3,1,2,4,6]=>27104
[5,3,1,2,6,4]=>27006
[5,3,1,4,2,6]=>26829
[5,3,1,4,6,2]=>26544
[5,3,1,6,2,4]=>26598
[5,3,1,6,4,2]=>26411
[5,3,2,1,4,6]=>26642
[5,3,2,1,6,4]=>26544
[5,3,2,4,1,6]=>26103
[5,3,2,4,6,1]=>25653
[5,3,2,6,1,4]=>25872
[5,3,2,6,4,1]=>25520
[5,3,4,1,2,6]=>25938
[5,3,4,1,6,2]=>25653
[5,3,4,2,1,6]=>25674
[5,3,4,2,6,1]=>25224
[5,3,4,6,1,2]=>24981
[5,3,4,6,2,1]=>24816
[5,3,6,1,2,4]=>25520
[5,3,6,1,4,2]=>25333
[5,3,6,2,1,4]=>25256
[5,3,6,2,4,1]=>24904
[5,3,6,4,1,2]=>24794
[5,3,6,4,2,1]=>24629
[5,4,1,2,3,6]=>26565
[5,4,1,2,6,3]=>26390
[5,4,1,3,2,6]=>26400
[5,4,1,3,6,2]=>26115
[5,4,1,6,2,3]=>25982
[5,4,1,6,3,2]=>25872
[5,4,2,1,3,6]=>26103
[5,4,2,1,6,3]=>25928
[5,4,2,3,1,6]=>25674
[5,4,2,3,6,1]=>25224
[5,4,2,6,1,3]=>25256
[5,4,2,6,3,1]=>24981
[5,4,3,1,2,6]=>25674
[5,4,3,1,6,2]=>25389
[5,4,3,2,1,6]=>25410
[5,4,3,2,6,1]=>24960
[5,4,3,6,1,2]=>24717
[5,4,3,6,2,1]=>24552
[5,4,6,1,2,3]=>24904
[5,4,6,1,3,2]=>24794
[5,4,6,2,1,3]=>24640
[5,4,6,2,3,1]=>24365
[5,4,6,3,1,2]=>24365
[5,4,6,3,2,1]=>24200
[5,6,1,2,3,4]=>25872
[5,6,1,2,4,3]=>25795
[5,6,1,3,2,4]=>25707
[5,6,1,3,4,2]=>25520
[5,6,1,4,2,3]=>25520
[5,6,1,4,3,2]=>25410
[5,6,2,1,3,4]=>25410
[5,6,2,1,4,3]=>25333
[5,6,2,3,1,4]=>24981
[5,6,2,3,4,1]=>24629
[5,6,2,4,1,3]=>24794
[5,6,2,4,3,1]=>24519
[5,6,3,1,2,4]=>24981
[5,6,3,1,4,2]=>24794
[5,6,3,2,1,4]=>24717
[5,6,3,2,4,1]=>24365
[5,6,3,4,1,2]=>24255
[5,6,3,4,2,1]=>24090
[5,6,4,1,2,3]=>24629
[5,6,4,1,3,2]=>24519
[5,6,4,2,1,3]=>24365
[5,6,4,2,3,1]=>24090
[5,6,4,3,1,2]=>24090
[5,6,4,3,2,1]=>23925
[6,1,2,3,4,5]=>28304
[6,1,2,3,5,4]=>28248
[6,1,2,4,3,5]=>28194
[6,1,2,4,5,3]=>28061
[6,1,2,5,3,4]=>28061
[6,1,2,5,4,3]=>27984
[6,1,3,2,4,5]=>28040
[6,1,3,2,5,4]=>27984
[6,1,3,4,2,5]=>27765
[6,1,3,4,5,2]=>27522
[6,1,3,5,2,4]=>27632
[6,1,3,5,4,2]=>27445
[6,1,4,2,3,5]=>27765
[6,1,4,2,5,3]=>27632
[6,1,4,3,2,5]=>27600
[6,1,4,3,5,2]=>27357
[6,1,4,5,2,3]=>27280
[6,1,4,5,3,2]=>27170
[6,1,5,2,3,4]=>27522
[6,1,5,2,4,3]=>27445
[6,1,5,3,2,4]=>27357
[6,1,5,3,4,2]=>27170
[6,1,5,4,2,3]=>27170
[6,1,5,4,3,2]=>27060
[6,2,1,3,4,5]=>27380
[6,2,1,3,5,4]=>27324
[6,2,1,4,3,5]=>27270
[6,2,1,4,5,3]=>27137
[6,2,1,5,3,4]=>27137
[6,2,1,5,4,3]=>27060
[6,2,3,1,4,5]=>26654
[6,2,3,1,5,4]=>26598
[6,2,3,4,1,5]=>26115
[6,2,3,4,5,1]=>25707
[6,2,3,5,1,4]=>25982
[6,2,3,5,4,1]=>25630
[6,2,4,1,3,5]=>26379
[6,2,4,1,5,3]=>26246
[6,2,4,3,1,5]=>25950
[6,2,4,3,5,1]=>25542
[6,2,4,5,1,3]=>25630
[6,2,4,5,3,1]=>25355
[6,2,5,1,3,4]=>26136
[6,2,5,1,4,3]=>26059
[6,2,5,3,1,4]=>25707
[6,2,5,3,4,1]=>25355
[6,2,5,4,1,3]=>25520
[6,2,5,4,3,1]=>25245
[6,3,1,2,4,5]=>26654
[6,3,1,2,5,4]=>26598
[6,3,1,4,2,5]=>26379
[6,3,1,4,5,2]=>26136
[6,3,1,5,2,4]=>26246
[6,3,1,5,4,2]=>26059
[6,3,2,1,4,5]=>26192
[6,3,2,1,5,4]=>26136
[6,3,2,4,1,5]=>25653
[6,3,2,4,5,1]=>25245
[6,3,2,5,1,4]=>25520
[6,3,2,5,4,1]=>25168
[6,3,4,1,2,5]=>25488
[6,3,4,1,5,2]=>25245
[6,3,4,2,1,5]=>25224
[6,3,4,2,5,1]=>24816
[6,3,4,5,1,2]=>24629
[6,3,4,5,2,1]=>24464
[6,3,5,1,2,4]=>25245
[6,3,5,1,4,2]=>25058
[6,3,5,2,1,4]=>24981
[6,3,5,2,4,1]=>24629
[6,3,5,4,1,2]=>24519
[6,3,5,4,2,1]=>24354
[6,4,1,2,3,5]=>26115
[6,4,1,2,5,3]=>25982
[6,4,1,3,2,5]=>25950
[6,4,1,3,5,2]=>25707
[6,4,1,5,2,3]=>25630
[6,4,1,5,3,2]=>25520
[6,4,2,1,3,5]=>25653
[6,4,2,1,5,3]=>25520
[6,4,2,3,1,5]=>25224
[6,4,2,3,5,1]=>24816
[6,4,2,5,1,3]=>24904
[6,4,2,5,3,1]=>24629
[6,4,3,1,2,5]=>25224
[6,4,3,1,5,2]=>24981
[6,4,3,2,1,5]=>24960
[6,4,3,2,5,1]=>24552
[6,4,3,5,1,2]=>24365
[6,4,3,5,2,1]=>24200
[6,4,5,1,2,3]=>24629
[6,4,5,1,3,2]=>24519
[6,4,5,2,1,3]=>24365
[6,4,5,2,3,1]=>24090
[6,4,5,3,1,2]=>24090
[6,4,5,3,2,1]=>23925
[6,5,1,2,3,4]=>25707
[6,5,1,2,4,3]=>25630
[6,5,1,3,2,4]=>25542
[6,5,1,3,4,2]=>25355
[6,5,1,4,2,3]=>25355
[6,5,1,4,3,2]=>25245
[6,5,2,1,3,4]=>25245
[6,5,2,1,4,3]=>25168
[6,5,2,3,1,4]=>24816
[6,5,2,3,4,1]=>24464
[6,5,2,4,1,3]=>24629
[6,5,2,4,3,1]=>24354
[6,5,3,1,2,4]=>24816
[6,5,3,1,4,2]=>24629
[6,5,3,2,1,4]=>24552
[6,5,3,2,4,1]=>24200
[6,5,3,4,1,2]=>24090
[6,5,3,4,2,1]=>23925
[6,5,4,1,2,3]=>24464
[6,5,4,1,3,2]=>24354
[6,5,4,2,1,3]=>24200
[6,5,4,2,3,1]=>23925
[6,5,4,3,1,2]=>23925
[6,5,4,3,2,1]=>23760
[1,2,3,4,5,6,7]=>467181
[1,2,3,4,5,7,6]=>466851
[1,2,3,4,6,5,7]=>466635
[1,2,3,4,6,7,5]=>465885
[1,2,3,4,7,5,6]=>465885
[1,2,3,4,7,6,5]=>465465
[1,2,3,5,4,6,7]=>466180
[1,2,3,5,4,7,6]=>465850
[1,2,3,5,6,4,7]=>464906
[1,2,3,5,6,7,4]=>463610
[1,2,3,5,7,4,6]=>464156
[1,2,3,5,7,6,4]=>463190
[1,2,3,6,4,5,7]=>464906
[1,2,3,6,4,7,5]=>464156
[1,2,3,6,5,4,7]=>464178
[1,2,3,6,5,7,4]=>462882
[1,2,3,6,7,4,5]=>462462
[1,2,3,6,7,5,4]=>461916
[1,2,3,7,4,5,6]=>463610
[1,2,3,7,4,6,5]=>463190
[1,2,3,7,5,4,6]=>462882
[1,2,3,7,5,6,4]=>461916
[1,2,3,7,6,4,5]=>461916
[1,2,3,7,6,5,4]=>461370
[1,2,4,3,5,6,7]=>465036
[1,2,4,3,5,7,6]=>464706
[1,2,4,3,6,5,7]=>464490
[1,2,4,3,6,7,5]=>463740
[1,2,4,3,7,5,6]=>463740
[1,2,4,3,7,6,5]=>463320
[1,2,4,5,3,6,7]=>462605
[1,2,4,5,3,7,6]=>462275
[1,2,4,5,6,3,7]=>460330
[1,2,4,5,6,7,3]=>458306
[1,2,4,5,7,3,6]=>459580
[1,2,4,5,7,6,3]=>457886
[1,2,4,6,3,5,7]=>461331
[1,2,4,6,3,7,5]=>460581
[1,2,4,6,5,3,7]=>459602
[1,2,4,6,5,7,3]=>457578
[1,2,4,6,7,3,5]=>457886
[1,2,4,6,7,5,3]=>456612
[1,2,4,7,3,5,6]=>460035
[1,2,4,7,3,6,5]=>459615
[1,2,4,7,5,3,6]=>458306
[1,2,4,7,5,6,3]=>456612
[1,2,4,7,6,3,5]=>457340
[1,2,4,7,6,5,3]=>456066
[1,2,5,3,4,6,7]=>462605
[1,2,5,3,4,7,6]=>462275
[1,2,5,3,6,4,7]=>461331
[1,2,5,3,6,7,4]=>460035
[1,2,5,3,7,4,6]=>460581
[1,2,5,3,7,6,4]=>459615
[1,2,5,4,3,6,7]=>461175
[1,2,5,4,3,7,6]=>460845
[1,2,5,4,6,3,7]=>458900
[1,2,5,4,6,7,3]=>456876
[1,2,5,4,7,3,6]=>458150
[1,2,5,4,7,6,3]=>456456
[1,2,5,6,3,4,7]=>458172
[1,2,5,6,3,7,4]=>456876
[1,2,5,6,4,3,7]=>457171
[1,2,5,6,4,7,3]=>455147
[1,2,5,6,7,3,4]=>454181
[1,2,5,6,7,4,3]=>453453
[1,2,5,7,3,4,6]=>456876
[1,2,5,7,3,6,4]=>455910
[1,2,5,7,4,3,6]=>455875
[1,2,5,7,4,6,3]=>454181
[1,2,5,7,6,3,4]=>453635
[1,2,5,7,6,4,3]=>452907
[1,2,6,3,4,5,7]=>460330
[1,2,6,3,4,7,5]=>459580
[1,2,6,3,5,4,7]=>459602
[1,2,6,3,5,7,4]=>458306
[1,2,6,3,7,4,5]=>457886
[1,2,6,3,7,5,4]=>457340
[1,2,6,4,3,5,7]=>458900
[1,2,6,4,3,7,5]=>458150
[1,2,6,4,5,3,7]=>457171
[1,2,6,4,5,7,3]=>455147
[1,2,6,4,7,3,5]=>455455
[1,2,6,4,7,5,3]=>454181
[1,2,6,5,3,4,7]=>457171
[1,2,6,5,3,7,4]=>455875
[1,2,6,5,4,3,7]=>456170
[1,2,6,5,4,7,3]=>454146
[1,2,6,5,7,3,4]=>453180
[1,2,6,5,7,4,3]=>452452
[1,2,6,7,3,4,5]=>454181
[1,2,6,7,3,5,4]=>453635
[1,2,6,7,4,3,5]=>453180
[1,2,6,7,4,5,3]=>451906
[1,2,6,7,5,3,4]=>451906
[1,2,6,7,5,4,3]=>451178
[1,2,7,3,4,5,6]=>458306
[1,2,7,3,4,6,5]=>457886
[1,2,7,3,5,4,6]=>457578
[1,2,7,3,5,6,4]=>456612
[1,2,7,3,6,4,5]=>456612
[1,2,7,3,6,5,4]=>456066
[1,2,7,4,3,5,6]=>456876
[1,2,7,4,3,6,5]=>456456
[1,2,7,4,5,3,6]=>455147
[1,2,7,4,5,6,3]=>453453
[1,2,7,4,6,3,5]=>454181
[1,2,7,4,6,5,3]=>452907
[1,2,7,5,3,4,6]=>455147
[1,2,7,5,3,6,4]=>454181
[1,2,7,5,4,3,6]=>454146
[1,2,7,5,4,6,3]=>452452
[1,2,7,5,6,3,4]=>451906
[1,2,7,5,6,4,3]=>451178
[1,2,7,6,3,4,5]=>453453
[1,2,7,6,3,5,4]=>452907
[1,2,7,6,4,3,5]=>452452
[1,2,7,6,4,5,3]=>451178
[1,2,7,6,5,3,4]=>451178
[1,2,7,6,5,4,3]=>450450
[1,3,2,4,5,6,7]=>461175
[1,3,2,4,5,7,6]=>460845
[1,3,2,4,6,5,7]=>460629
[1,3,2,4,6,7,5]=>459879
[1,3,2,4,7,5,6]=>459879
[1,3,2,4,7,6,5]=>459459
[1,3,2,5,4,6,7]=>460174
[1,3,2,5,4,7,6]=>459844
[1,3,2,5,6,4,7]=>458900
[1,3,2,5,6,7,4]=>457604
[1,3,2,5,7,4,6]=>458150
[1,3,2,5,7,6,4]=>457184
[1,3,2,6,4,5,7]=>458900
[1,3,2,6,4,7,5]=>458150
[1,3,2,6,5,4,7]=>458172
[1,3,2,6,5,7,4]=>456876
[1,3,2,6,7,4,5]=>456456
[1,3,2,6,7,5,4]=>455910
[1,3,2,7,4,5,6]=>457604
[1,3,2,7,4,6,5]=>457184
[1,3,2,7,5,4,6]=>456876
[1,3,2,7,5,6,4]=>455910
[1,3,2,7,6,4,5]=>455910
[1,3,2,7,6,5,4]=>455364
[1,3,4,2,5,6,7]=>455598
[1,3,4,2,5,7,6]=>455268
[1,3,4,2,6,5,7]=>455052
[1,3,4,2,6,7,5]=>454302
[1,3,4,2,7,5,6]=>454302
[1,3,4,2,7,6,5]=>453882
[1,3,4,5,2,6,7]=>451022
[1,3,4,5,2,7,6]=>450692
[1,3,4,5,6,2,7]=>447317
[1,3,4,5,6,7,2]=>444292
[1,3,4,5,7,2,6]=>446567
[1,3,4,5,7,6,2]=>443872
[1,3,4,6,2,5,7]=>449748
[1,3,4,6,2,7,5]=>448998
[1,3,4,6,5,2,7]=>446589
[1,3,4,6,5,7,2]=>443564
[1,3,4,6,7,2,5]=>444873
[1,3,4,6,7,5,2]=>442598
[1,3,4,7,2,5,6]=>448452
[1,3,4,7,2,6,5]=>448032
[1,3,4,7,5,2,6]=>445293
[1,3,4,7,5,6,2]=>442598
[1,3,4,7,6,2,5]=>444327
[1,3,4,7,6,5,2]=>442052
[1,3,5,2,4,6,7]=>453167
[1,3,5,2,4,7,6]=>452837
[1,3,5,2,6,4,7]=>451893
[1,3,5,2,6,7,4]=>450597
[1,3,5,2,7,4,6]=>451143
[1,3,5,2,7,6,4]=>450177
[1,3,5,4,2,6,7]=>449592
[1,3,5,4,2,7,6]=>449262
[1,3,5,4,6,2,7]=>445887
[1,3,5,4,6,7,2]=>442862
[1,3,5,4,7,2,6]=>445137
[1,3,5,4,7,6,2]=>442442
[1,3,5,6,2,4,7]=>446589
[1,3,5,6,2,7,4]=>445293
[1,3,5,6,4,2,7]=>444158
[1,3,5,6,4,7,2]=>441133
[1,3,5,6,7,2,4]=>441168
[1,3,5,6,7,4,2]=>439439
[1,3,5,7,2,4,6]=>445293
[1,3,5,7,2,6,4]=>444327
[1,3,5,7,4,2,6]=>442862
[1,3,5,7,4,6,2]=>440167
[1,3,5,7,6,2,4]=>440622
[1,3,5,7,6,4,2]=>438893
[1,3,6,2,4,5,7]=>450892
[1,3,6,2,4,7,5]=>450142
[1,3,6,2,5,4,7]=>450164
[1,3,6,2,5,7,4]=>448868
[1,3,6,2,7,4,5]=>448448
[1,3,6,2,7,5,4]=>447902
[1,3,6,4,2,5,7]=>447317
[1,3,6,4,2,7,5]=>446567
[1,3,6,4,5,2,7]=>444158
[1,3,6,4,5,7,2]=>441133
[1,3,6,4,7,2,5]=>442442
[1,3,6,4,7,5,2]=>440167
[1,3,6,5,2,4,7]=>445588
[1,3,6,5,2,7,4]=>444292
[1,3,6,5,4,2,7]=>443157
[1,3,6,5,4,7,2]=>440132
[1,3,6,5,7,2,4]=>440167
[1,3,6,5,7,4,2]=>438438
[1,3,6,7,2,4,5]=>442598
[1,3,6,7,2,5,4]=>442052
[1,3,6,7,4,2,5]=>440167
[1,3,6,7,4,5,2]=>437892
[1,3,6,7,5,2,4]=>438893
[1,3,6,7,5,4,2]=>437164
[1,3,7,2,4,5,6]=>448868
[1,3,7,2,4,6,5]=>448448
[1,3,7,2,5,4,6]=>448140
[1,3,7,2,5,6,4]=>447174
[1,3,7,2,6,4,5]=>447174
[1,3,7,2,6,5,4]=>446628
[1,3,7,4,2,5,6]=>445293
[1,3,7,4,2,6,5]=>444873
[1,3,7,4,5,2,6]=>442134
[1,3,7,4,5,6,2]=>439439
[1,3,7,4,6,2,5]=>441168
[1,3,7,4,6,5,2]=>438893
[1,3,7,5,2,4,6]=>443564
[1,3,7,5,2,6,4]=>442598
[1,3,7,5,4,2,6]=>441133
[1,3,7,5,4,6,2]=>438438
[1,3,7,5,6,2,4]=>438893
[1,3,7,5,6,4,2]=>437164
[1,3,7,6,2,4,5]=>441870
[1,3,7,6,2,5,4]=>441324
[1,3,7,6,4,2,5]=>439439
[1,3,7,6,4,5,2]=>437164
[1,3,7,6,5,2,4]=>438165
[1,3,7,6,5,4,2]=>436436
[1,4,2,3,5,6,7]=>455598
[1,4,2,3,5,7,6]=>455268
[1,4,2,3,6,5,7]=>455052
[1,4,2,3,6,7,5]=>454302
[1,4,2,3,7,5,6]=>454302
[1,4,2,3,7,6,5]=>453882
[1,4,2,5,3,6,7]=>453167
[1,4,2,5,3,7,6]=>452837
[1,4,2,5,6,3,7]=>450892
[1,4,2,5,6,7,3]=>448868
[1,4,2,5,7,3,6]=>450142
[1,4,2,5,7,6,3]=>448448
[1,4,2,6,3,5,7]=>451893
[1,4,2,6,3,7,5]=>451143
[1,4,2,6,5,3,7]=>450164
[1,4,2,6,5,7,3]=>448140
[1,4,2,6,7,3,5]=>448448
[1,4,2,6,7,5,3]=>447174
[1,4,2,7,3,5,6]=>450597
[1,4,2,7,3,6,5]=>450177
[1,4,2,7,5,3,6]=>448868
[1,4,2,7,5,6,3]=>447174
[1,4,2,7,6,3,5]=>447902
[1,4,2,7,6,5,3]=>446628
[1,4,3,2,5,6,7]=>452166
[1,4,3,2,5,7,6]=>451836
[1,4,3,2,6,5,7]=>451620
[1,4,3,2,6,7,5]=>450870
[1,4,3,2,7,5,6]=>450870
[1,4,3,2,7,6,5]=>450450
[1,4,3,5,2,6,7]=>447590
[1,4,3,5,2,7,6]=>447260
[1,4,3,5,6,2,7]=>443885
[1,4,3,5,6,7,2]=>440860
[1,4,3,5,7,2,6]=>443135
[1,4,3,5,7,6,2]=>440440
[1,4,3,6,2,5,7]=>446316
[1,4,3,6,2,7,5]=>445566
[1,4,3,6,5,2,7]=>443157
[1,4,3,6,5,7,2]=>440132
[1,4,3,6,7,2,5]=>441441
[1,4,3,6,7,5,2]=>439166
[1,4,3,7,2,5,6]=>445020
[1,4,3,7,2,6,5]=>444600
[1,4,3,7,5,2,6]=>441861
[1,4,3,7,5,6,2]=>439166
[1,4,3,7,6,2,5]=>440895
[1,4,3,7,6,5,2]=>438620
[1,4,5,2,3,6,7]=>446160
[1,4,5,2,3,7,6]=>445830
[1,4,5,2,6,3,7]=>443885
[1,4,5,2,6,7,3]=>441861
[1,4,5,2,7,3,6]=>443135
[1,4,5,2,7,6,3]=>441441
[1,4,5,3,2,6,7]=>444015
[1,4,5,3,2,7,6]=>443685
[1,4,5,3,6,2,7]=>440310
[1,4,5,3,6,7,2]=>437285
[1,4,5,3,7,2,6]=>439560
[1,4,5,3,7,6,2]=>436865
[1,4,5,6,2,3,7]=>438581
[1,4,5,6,2,7,3]=>436557
[1,4,5,6,3,2,7]=>437151
[1,4,5,6,3,7,2]=>434126
[1,4,5,6,7,2,3]=>432432
[1,4,5,6,7,3,2]=>431431
[1,4,5,7,2,3,6]=>437285
[1,4,5,7,2,6,3]=>435591
[1,4,5,7,3,2,6]=>435855
[1,4,5,7,3,6,2]=>433160
[1,4,5,7,6,2,3]=>431886
[1,4,5,7,6,3,2]=>430885
[1,4,6,2,3,5,7]=>443885
[1,4,6,2,3,7,5]=>443135
[1,4,6,2,5,3,7]=>442156
[1,4,6,2,5,7,3]=>440132
[1,4,6,2,7,3,5]=>440440
[1,4,6,2,7,5,3]=>439166
[1,4,6,3,2,5,7]=>441740
[1,4,6,3,2,7,5]=>440990
[1,4,6,3,5,2,7]=>438581
[1,4,6,3,5,7,2]=>435556
[1,4,6,3,7,2,5]=>436865
[1,4,6,3,7,5,2]=>434590
[1,4,6,5,2,3,7]=>437580
[1,4,6,5,2,7,3]=>435556
[1,4,6,5,3,2,7]=>436150
                    

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$F_{1} = q$

$F_{2} = q^{8} + q^{9}$

$F_{3} = q^{45} + 2\ q^{47} + q^{50} + q^{54} + q^{55}$

$F_{4} = q^{672} + 3\ q^{686} + q^{700} + 2\ q^{708} + 2\ q^{728} + q^{735} + 2\ q^{736} + 2\ q^{750} + 2\ q^{763} + q^{800} + q^{805} + q^{840} + 2\ q^{848} + q^{861} + q^{870} + q^{875}$

$F_{5} = q^{2100} + 4\ q^{2124} + 3\ q^{2148} + 3\ q^{2163} + 2\ q^{2187} + 3\ q^{2190} + 3\ q^{2205} + 2\ q^{2212} + 2\ q^{2214} + 6\ q^{2229} + 4\ q^{2254} + 2\ q^{2268} + 2\ q^{2278} + q^{2295} + 5\ q^{2310} + 4\ q^{2320} + 2\ q^{2340} + q^{2352} + 4\ q^{2355} + 2\ q^{2359} + 2\ q^{2376} + 2\ q^{2379} + 2\ q^{2380} + 4\ q^{2394} + 4\ q^{2404} + 2\ q^{2436} + 2\ q^{2443} + q^{2450} + q^{2457} + 4\ q^{2460} + 2\ q^{2470} + 2\ q^{2485} + 2\ q^{2502} + 2\ q^{2534} + 2\ q^{2541} + q^{2625} + 2\ q^{2635} + q^{2652} + q^{2660} + q^{2667} + q^{2700} + 3\ q^{2715} + q^{2730} + 2\ q^{2740} + 2\ q^{2754} + 2\ q^{2764} + q^{2772} + 2\ q^{2779} + 2\ q^{2796} + q^{2828} + 2\ q^{2835} + 2\ q^{2845} + q^{2862} + q^{2870} + q^{2877}$

$F_{6} = q^{23760} + 5\ q^{23925} + 6\ q^{24090} + 4\ q^{24200} + q^{24255} + 4\ q^{24354} + 6\ q^{24365} + 4\ q^{24464} + 6\ q^{24519} + 3\ q^{24552} + 12\ q^{24629} + q^{24640} + 2\ q^{24717} + 6\ q^{24794} + 6\ q^{24816} + 4\ q^{24904} + q^{24948} + 2\ q^{24960} + 8\ q^{24981} + 4\ q^{25058} + 4\ q^{25168} + 6\ q^{25224} + 10\ q^{25245} + 2\ q^{25256} + 4\ q^{25333} + 6\ q^{25355} + 2\ q^{25389} + 6\ q^{25410} + 2\ q^{25488} + 14\ q^{25520} + 3\ q^{25542} + 7\ q^{25630} + 8\ q^{25653} + 4\ q^{25674} + 9\ q^{25707} + 3\ q^{25795} + 5\ q^{25872} + 2\ q^{25928} + 3\ q^{25938} + 4\ q^{25949} + 4\ q^{25950} + 8\ q^{25982} + 6\ q^{26059} + 2\ q^{26082} + 3\ q^{26103} + 6\ q^{26115} + 10\ q^{26136} + 4\ q^{26192} + 6\ q^{26246} + 3\ q^{26334} + 2\ q^{26367} + 8\ q^{26379} + 2\ q^{26390} + 3\ q^{26400} + 6\ q^{26411} + 6\ q^{26544} + 3\ q^{26565} + 6\ q^{26598} + 2\ q^{26642} + 8\ q^{26654} + 2\ q^{26664} + 6\ q^{26829} + 2\ q^{26950} + 4\ q^{27006} + 3\ q^{27027} + 4\ q^{27060} + 4\ q^{27083} + 4\ q^{27104} + 6\ q^{27137} + 6\ q^{27170} + q^{27216} + 2\ q^{27258} + 6\ q^{27270} + 2\ q^{27280} + 3\ q^{27324} + 2\ q^{27335} + 4\ q^{27357} + 2\ q^{27368} + 2\ q^{27380} + 2\ q^{27412} + 8\ q^{27445} + 4\ q^{27489} + 6\ q^{27522} + 4\ q^{27545} + q^{27555} + 2\ q^{27600} + 8\ q^{27632} + 3\ q^{27678} + 7\ q^{27720} + 4\ q^{27732} + 6\ q^{27765} + 4\ q^{27797} + 4\ q^{27830} + 2\ q^{27874} + 2\ q^{27930} + 2\ q^{27951} + 8\ q^{27984} + 2\ q^{28028} + 4\ q^{28040} + 2\ q^{28050} + 8\ q^{28061} + 2\ q^{28084} + q^{28140} + 2\ q^{28161} + q^{28182} + 4\ q^{28194} + 4\ q^{28215} + 2\ q^{28248} + 2\ q^{28259} + 4\ q^{28304} + 4\ q^{28336} + 2\ q^{28392} + 2\ q^{28404} + 4\ q^{28413} + 2\ q^{28446} + 8\ q^{28469} + 2\ q^{28479} + 2\ q^{28490} + 4\ q^{28644} + 4\ q^{28656} + 4\ q^{28754} + 2\ q^{28875} + 6\ q^{28952} + 2\ q^{29008} + 2\ q^{29062} + 2\ q^{29064} + 4\ q^{29085} + 3\ q^{29106} + 4\ q^{29139} + 2\ q^{29162} + 2\ q^{29183} + 4\ q^{29195} + q^{29260} + q^{29295} + 2\ q^{29328} + q^{29337} + 4\ q^{29370} + 2\ q^{29382} + 2\ q^{29414} + 2\ q^{29470} + 2\ q^{29480} + 2\ q^{29547} + 2\ q^{29645} + 2\ q^{29790} + 2\ q^{29832} + 2\ q^{30030} + 4\ q^{30086} + 2\ q^{30184} + 2\ q^{30219} + 2\ q^{30261} + q^{30800} + 3\ q^{30877} + q^{30954} + 2\ q^{31010} + 2\ q^{31064} + 2\ q^{31120} + 2\ q^{31185} + 2\ q^{31197} + 6\ q^{31295} + 3\ q^{31405} + q^{31416} + q^{31440} + 2\ q^{31472} + 4\ q^{31482} + 4\ q^{31570} + 2\ q^{31592} + q^{31605} + 4\ q^{31647} + 2\ q^{31680} + 2\ q^{31725} + 6\ q^{31757} + 4\ q^{31890} + q^{31944} + 2\ q^{32000} + q^{32010} + q^{32032} + 4\ q^{32109} + 4\ q^{32165} + 3\ q^{32175} + 4\ q^{32186} + 2\ q^{32296} + 2\ q^{32319} + q^{32340} + 2\ q^{32352} + 4\ q^{32373} + 4\ q^{32429} + 2\ q^{32450} + 2\ q^{32604} + 2\ q^{32616} + 2\ q^{32648} + 2\ q^{32704} + 2\ q^{32714} + q^{32760} + 2\ q^{32781} + q^{32802} + 2\ q^{32879} + 2\ q^{33024} + 2\ q^{33066} + q^{33110} + 3\ q^{33187} + 2\ q^{33264} + 4\ q^{33320} + 2\ q^{33374} + q^{33418} + 2\ q^{33430} + q^{33453} + 2\ q^{33495} + 2\ q^{33507} + 2\ q^{33605} + q^{33726} + q^{33750} + 2\ q^{33782} + q^{33792} + q^{33880} + q^{33915} + q^{33957}$

Description

The sum of all $1/(i+\pi(i))$ for a permutation $\pi$ times the lcm of all possible values among permutations of the same length.
It turns out that the least common multiple of all values is [1], so this statistic is given by
$$ k \cdot \sum_{i=1}^n \frac{1}{i+\pi(i)}$$
where $\pi$ is a permutation of length $n$ and $k = \operatorname{lcm}\{ 1,\dots,2n\}$.

References

[1] a(n) = lcm1, 2, ..., 2*n. OEIS:A099996

Code

def statistic(pi):
    n = len(pi)
    return sum( 1/(i+pi(i)) for i in [1,n] ) * lcm(i for i in [1 .. 2*n] )

Created

Nov 19, 2018 at 11:44 by Christian Stump

Updated

Nov 19, 2018 at 11:44 by Christian Stump