Identifier
Values
=>
Cc0002;cc-rep
[]=>0
[1]=>1
[2]=>3
[1,1]=>3
[3]=>6
[2,1]=>5
[1,1,1]=>6
[4]=>10
[3,1]=>8
[2,2]=>8
[2,1,1]=>8
[1,1,1,1]=>10
[5]=>15
[4,1]=>12
[3,2]=>11
[3,1,1]=>11
[2,2,1]=>11
[2,1,1,1]=>12
[1,1,1,1,1]=>15
[6]=>21
[5,1]=>17
[4,2]=>15
[4,1,1]=>15
[3,3]=>15
[3,2,1]=>14
[3,1,1,1]=>15
[2,2,2]=>15
[2,2,1,1]=>15
[2,1,1,1,1]=>17
[1,1,1,1,1,1]=>21
[7]=>28
[6,1]=>23
[5,2]=>20
[5,1,1]=>20
[4,3]=>19
[4,2,1]=>18
[4,1,1,1]=>19
[3,3,1]=>18
[3,2,2]=>18
[3,2,1,1]=>18
[3,1,1,1,1]=>20
[2,2,2,1]=>19
[2,2,1,1,1]=>20
[2,1,1,1,1,1]=>23
[1,1,1,1,1,1,1]=>28
[8]=>36
[7,1]=>30
[6,2]=>26
[6,1,1]=>26
[5,3]=>24
[5,2,1]=>23
[5,1,1,1]=>24
[4,4]=>24
[4,3,1]=>22
[4,2,2]=>22
[4,2,1,1]=>22
[4,1,1,1,1]=>24
[3,3,2]=>22
[3,3,1,1]=>22
[3,2,2,1]=>22
[3,2,1,1,1]=>23
[3,1,1,1,1,1]=>26
[2,2,2,2]=>24
[2,2,2,1,1]=>24
[2,2,1,1,1,1]=>26
[2,1,1,1,1,1,1]=>30
[1,1,1,1,1,1,1,1]=>36
[9]=>45
[8,1]=>38
[7,2]=>33
[7,1,1]=>33
[6,3]=>30
[6,2,1]=>29
[6,1,1,1]=>30
[5,4]=>29
[5,3,1]=>27
[5,2,2]=>27
[5,2,1,1]=>27
[5,1,1,1,1]=>29
[4,4,1]=>27
[4,3,2]=>26
[4,3,1,1]=>26
[4,2,2,1]=>26
[4,2,1,1,1]=>27
[4,1,1,1,1,1]=>30
[3,3,3]=>27
[3,3,2,1]=>26
[3,3,1,1,1]=>27
[3,2,2,2]=>27
[3,2,2,1,1]=>27
[3,2,1,1,1,1]=>29
[3,1,1,1,1,1,1]=>33
[2,2,2,2,1]=>29
[2,2,2,1,1,1]=>30
[2,2,1,1,1,1,1]=>33
[2,1,1,1,1,1,1,1]=>38
[1,1,1,1,1,1,1,1,1]=>45
[10]=>55
[9,1]=>47
[8,2]=>41
[8,1,1]=>41
[7,3]=>37
[7,2,1]=>36
[7,1,1,1]=>37
[6,4]=>35
[6,3,1]=>33
[6,2,2]=>33
[6,2,1,1]=>33
[6,1,1,1,1]=>35
[5,5]=>35
[5,4,1]=>32
[5,3,2]=>31
[5,3,1,1]=>31
[5,2,2,1]=>31
[5,2,1,1,1]=>32
[5,1,1,1,1,1]=>35
[4,4,2]=>31
[4,4,1,1]=>31
[4,3,3]=>31
[4,3,2,1]=>30
[4,3,1,1,1]=>31
[4,2,2,2]=>31
[4,2,2,1,1]=>31
[4,2,1,1,1,1]=>33
[4,1,1,1,1,1,1]=>37
[3,3,3,1]=>31
[3,3,2,2]=>31
[3,3,2,1,1]=>31
[3,3,1,1,1,1]=>33
[3,2,2,2,1]=>32
[3,2,2,1,1,1]=>33
[3,2,1,1,1,1,1]=>36
[3,1,1,1,1,1,1,1]=>41
[2,2,2,2,2]=>35
[2,2,2,2,1,1]=>35
[2,2,2,1,1,1,1]=>37
[2,2,1,1,1,1,1,1]=>41
[2,1,1,1,1,1,1,1,1]=>47
[1,1,1,1,1,1,1,1,1,1]=>55
[11]=>66
[10,1]=>57
[9,2]=>50
[9,1,1]=>50
[8,3]=>45
[8,2,1]=>44
[8,1,1,1]=>45
[7,4]=>42
[7,3,1]=>40
[7,2,2]=>40
[7,2,1,1]=>40
[7,1,1,1,1]=>42
[6,5]=>41
[6,4,1]=>38
[6,3,2]=>37
[6,3,1,1]=>37
[6,2,2,1]=>37
[6,2,1,1,1]=>38
[6,1,1,1,1,1]=>41
[5,5,1]=>38
[5,4,2]=>36
[5,4,1,1]=>36
[5,3,3]=>36
[5,3,2,1]=>35
[5,3,1,1,1]=>36
[5,2,2,2]=>36
[5,2,2,1,1]=>36
[5,2,1,1,1,1]=>38
[5,1,1,1,1,1,1]=>42
[4,4,3]=>36
[4,4,2,1]=>35
[4,4,1,1,1]=>36
[4,3,3,1]=>35
[4,3,2,2]=>35
[4,3,2,1,1]=>35
[4,3,1,1,1,1]=>37
[4,2,2,2,1]=>36
[4,2,2,1,1,1]=>37
[4,2,1,1,1,1,1]=>40
[4,1,1,1,1,1,1,1]=>45
[3,3,3,2]=>36
[3,3,3,1,1]=>36
[3,3,2,2,1]=>36
[3,3,2,1,1,1]=>37
[3,3,1,1,1,1,1]=>40
[3,2,2,2,2]=>38
[3,2,2,2,1,1]=>38
[3,2,2,1,1,1,1]=>40
[3,2,1,1,1,1,1,1]=>44
[3,1,1,1,1,1,1,1,1]=>50
[2,2,2,2,2,1]=>41
[2,2,2,2,1,1,1]=>42
[2,2,2,1,1,1,1,1]=>45
[2,2,1,1,1,1,1,1,1]=>50
[2,1,1,1,1,1,1,1,1,1]=>57
[1,1,1,1,1,1,1,1,1,1,1]=>66
[12]=>78
[11,1]=>68
[10,2]=>60
[10,1,1]=>60
[9,3]=>54
[9,2,1]=>53
[9,1,1,1]=>54
[8,4]=>50
[8,3,1]=>48
[8,2,2]=>48
[8,2,1,1]=>48
[8,1,1,1,1]=>50
[7,5]=>48
[7,4,1]=>45
[7,3,2]=>44
[7,3,1,1]=>44
[7,2,2,1]=>44
[7,2,1,1,1]=>45
[7,1,1,1,1,1]=>48
[6,6]=>48
[6,5,1]=>44
[6,4,2]=>42
[6,4,1,1]=>42
[6,3,3]=>42
[6,3,2,1]=>41
[6,3,1,1,1]=>42
[6,2,2,2]=>42
[6,2,2,1,1]=>42
[6,2,1,1,1,1]=>44
[6,1,1,1,1,1,1]=>48
[5,5,2]=>42
[5,5,1,1]=>42
[5,4,3]=>41
[5,4,2,1]=>40
[5,4,1,1,1]=>41
[5,3,3,1]=>40
[5,3,2,2]=>40
[5,3,2,1,1]=>40
[5,3,1,1,1,1]=>42
[5,2,2,2,1]=>41
[5,2,2,1,1,1]=>42
[5,2,1,1,1,1,1]=>45
[5,1,1,1,1,1,1,1]=>50
[4,4,4]=>42
[4,4,3,1]=>40
[4,4,2,2]=>40
[4,4,2,1,1]=>40
[4,4,1,1,1,1]=>42
[4,3,3,2]=>40
[4,3,3,1,1]=>40
[4,3,2,2,1]=>40
[4,3,2,1,1,1]=>41
[4,3,1,1,1,1,1]=>44
[4,2,2,2,2]=>42
[4,2,2,2,1,1]=>42
[4,2,2,1,1,1,1]=>44
[4,2,1,1,1,1,1,1]=>48
[4,1,1,1,1,1,1,1,1]=>54
[3,3,3,3]=>42
[3,3,3,2,1]=>41
[3,3,3,1,1,1]=>42
[3,3,2,2,2]=>42
[3,3,2,2,1,1]=>42
[3,3,2,1,1,1,1]=>44
[3,3,1,1,1,1,1,1]=>48
[3,2,2,2,2,1]=>44
[3,2,2,2,1,1,1]=>45
[3,2,2,1,1,1,1,1]=>48
[3,2,1,1,1,1,1,1,1]=>53
[3,1,1,1,1,1,1,1,1,1]=>60
[2,2,2,2,2,2]=>48
[2,2,2,2,2,1,1]=>48
[2,2,2,2,1,1,1,1]=>50
[2,2,2,1,1,1,1,1,1]=>54
[2,2,1,1,1,1,1,1,1,1]=>60
[2,1,1,1,1,1,1,1,1,1,1]=>68
[1,1,1,1,1,1,1,1,1,1,1,1]=>78
[13]=>91
[12,1]=>80
[10,3]=>64
[9,4]=>59
[9,2,2]=>57
[8,5]=>56
[8,4,1]=>53
[8,3,2]=>52
[8,3,1,1]=>52
[7,6]=>55
[7,5,1]=>51
[7,4,2]=>49
[7,4,1,1]=>49
[7,3,3]=>49
[7,3,2,1]=>48
[6,6,1]=>51
[6,5,2]=>48
[6,5,1,1]=>48
[6,4,3]=>47
[6,4,2,1]=>46
[6,3,3,1]=>46
[6,3,2,2]=>46
[6,3,1,1,1,1]=>48
[6,2,2,1,1,1]=>48
[6,1,1,1,1,1,1,1]=>56
[5,5,3]=>47
[5,5,2,1]=>46
[5,4,4]=>47
[5,4,3,1]=>45
[5,4,2,2]=>45
[5,4,2,1,1]=>45
[5,4,1,1,1,1]=>47
[5,3,3,2]=>45
[5,3,3,1,1]=>45
[5,3,2,2,1]=>45
[5,3,2,1,1,1]=>46
[5,3,1,1,1,1,1]=>49
[5,2,2,2,1,1]=>47
[5,2,2,1,1,1,1]=>49
[5,2,1,1,1,1,1,1]=>53
[4,4,4,1]=>46
[4,4,3,2]=>45
[4,4,3,1,1]=>45
[4,4,2,2,1]=>45
[4,3,3,3]=>46
[4,3,3,2,1]=>45
[3,3,3,3,1]=>47
[3,3,3,2,2]=>47
[3,3,3,2,1,1]=>47
[3,3,2,2,2,1]=>48
[3,3,2,2,1,1,1]=>49
[3,3,2,1,1,1,1,1]=>52
[3,2,2,2,2,2]=>51
[3,2,2,2,2,1,1]=>51
[3,1,1,1,1,1,1,1,1,1,1]=>71
[2,2,2,2,2,2,1]=>55
[2,2,2,2,1,1,1,1,1]=>59
[1,1,1,1,1,1,1,1,1,1,1,1,1]=>91
[14]=>105
[13,1]=>93
[12,2]=>83
[12,1,1]=>83
[11,2,1]=>74
[10,2,2]=>67
[9,5]=>65
[8,6]=>63
[8,5,1]=>59
[8,4,2]=>57
[8,3,3]=>57
[8,3,1,1,1]=>57
[7,7]=>63
[7,6,1]=>58
[7,5,2]=>55
[7,4,3]=>54
[6,6,2]=>55
[6,6,1,1]=>55
[6,5,3]=>53
[6,5,1,1,1]=>53
[6,4,4]=>53
[6,4,2,2]=>51
[6,2,2,2,2]=>53
[6,1,1,1,1,1,1,1,1]=>65
[5,5,4]=>53
[5,5,1,1,1,1]=>53
[5,4,4,1]=>51
[5,4,3,2]=>50
[5,4,3,1,1]=>50
[5,4,2,2,1]=>50
[5,4,2,1,1,1]=>51
[5,4,1,1,1,1,1]=>54
[5,3,3,3]=>51
[5,3,3,2,1]=>50
[5,3,2,2,2]=>51
[5,3,2,2,1,1]=>51
[5,3,2,1,1,1,1]=>53
[5,3,1,1,1,1,1,1]=>57
[5,2,2,2,2,1]=>53
[5,2,2,1,1,1,1,1]=>57
[4,4,4,2]=>51
[4,4,4,1,1]=>51
[4,4,3,3]=>51
[4,4,3,2,1]=>50
[4,3,2,2,2,1]=>52
[3,3,3,3,2]=>53
[3,3,3,3,1,1]=>53
[3,3,3,2,2,1]=>53
[3,3,2,2,2,2]=>55
[3,3,1,1,1,1,1,1,1,1]=>67
[3,2,2,2,2,1,1,1]=>59
[2,2,2,2,2,2,2]=>63
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>105
[15]=>120
[14,1]=>107
[12,3]=>87
[11,2,2]=>78
[9,6]=>72
[9,5,1]=>68
[9,3,2,1]=>65
[8,7]=>71
[8,5,2]=>63
[7,5,3]=>60
[6,6,3]=>60
[6,5,4]=>59
[6,5,1,1,1,1]=>59
[6,4,3,1,1]=>56
[6,3,3,3]=>57
[6,3,1,1,1,1,1,1]=>63
[6,2,2,2,2,1]=>59
[5,5,5]=>60
[5,5,2,2,1]=>56
[5,4,3,3]=>56
[5,4,3,2,1]=>55
[5,4,3,1,1,1]=>56
[5,3,2,2,2,1]=>57
[5,3,2,2,1,1,1]=>58
[5,3,1,1,1,1,1,1,1]=>66
[4,4,4,3]=>57
[4,4,4,1,1,1]=>57
[4,3,3,3,2]=>57
[3,3,3,3,3]=>60
[3,3,3,3,2,1]=>59
[3,3,3,2,2,2]=>60
[2,2,2,2,2,2,2,1]=>71
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>120
[16]=>136
[15,1]=>122
[12,4]=>92
[12,1,1,1,1]=>92
[10,6]=>82
[8,8]=>80
[8,6,2]=>70
[8,5,3]=>68
[7,6,3]=>67
[7,5,3,1]=>64
[7,3,3,2,1]=>63
[6,6,4]=>66
[6,6,2,2]=>64
[6,5,5]=>66
[6,4,3,3]=>62
[5,5,3,3]=>62
[5,5,2,2,2]=>62
[5,4,4,3]=>62
[5,4,3,2,1,1]=>61
[5,4,2,2,2,1]=>62
[4,4,4,4]=>64
[4,4,4,2,2]=>62
[4,4,3,3,2]=>62
[4,4,2,2,2,2]=>64
[4,3,3,3,3]=>64
[4,3,3,3,2,1]=>63
[3,3,3,3,2,2]=>66
[3,3,3,3,1,1,1,1]=>68
[3,3,2,2,2,2,2]=>70
[2,2,2,2,2,2,2,2]=>80
[2,2,2,2,2,2,1,1,1,1]=>82
[2,2,2,2,1,1,1,1,1,1,1,1]=>92
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>136
[17]=>153
[16,1]=>138
[9,8]=>89
[8,8,1]=>83
[8,6,3]=>75
[7,5,3,2]=>69
[6,5,3,3]=>68
[6,5,2,2,2]=>68
[6,4,4,3]=>68
[6,4,4,1,1,1]=>68
[6,3,3,3,2]=>68
[6,3,3,3,1,1]=>68
[5,5,4,3]=>68
[5,5,4,1,1,1]=>68
[5,5,2,2,2,1]=>68
[5,4,4,4]=>69
[5,4,3,2,2,1]=>67
[5,3,3,3,2,1]=>68
[4,4,4,3,2]=>68
[4,4,4,3,1,1]=>68
[4,4,4,2,2,1]=>68
[4,4,3,3,3]=>69
[3,3,3,3,3,2]=>73
[3,2,2,2,2,2,2,2]=>83
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>125
[4,4,4,3,2,1]=>74
[5,4,3,3,2,1]=>73
[6,3,3,3,2,1]=>74
[6,5,2,2,2,1]=>74
[5,5,3,3,1,1]=>73
[6,5,4,1,1,1]=>74
[5,5,3,3,2]=>73
[5,5,4,2,2]=>73
[6,4,4,2,2]=>73
[6,5,4,3]=>74
[4,4,4,3,3]=>75
[4,4,4,4,2]=>75
[5,5,4,4]=>75
[6,4,4,4]=>75
[2,2,2,2,2,2,2,2,2]=>99
[3,3,3,3,3,3]=>81
[18]=>171
[6,2,2,2,2,2,2]=>81
[6,6,6]=>81
[4,2,2,2,2,2,2,2]=>87
[10,4,4]=>87
[9,6,3]=>84
[8,6,4]=>81
[10,8]=>99
[3,3,3,3,1,1,1,1,1,1]=>87
[9,9]=>99
[7,7,1,1,1,1]=>81
[5,4,4,3,2,1]=>79
[5,5,3,3,2,1]=>79
[5,5,4,2,2,1]=>79
[6,4,4,2,2,1]=>79
[5,5,4,3,1,1]=>79
[6,4,4,3,1,1]=>79
[6,5,3,3,1,1]=>79
[5,5,4,3,2]=>79
[6,4,4,3,2]=>79
[6,5,3,3,2]=>79
[6,5,4,2,2]=>79
[6,5,4,3,1]=>79
[6,5,4,1,1,1,1]=>81
[4,4,4,4,3]=>82
[4,3,3,3,3,3]=>85
[19]=>190
[7,2,2,2,2,2,2]=>88
[7,6,6]=>88
[5,2,2,2,2,2,2,2]=>92
[13,6]=>118
[11,4,4]=>98
[9,6,4]=>90
[8,5,4,2]=>83
[8,5,5,1]=>85
[5,5,4,3,2,1]=>85
[6,4,4,3,2,1]=>85
[6,5,3,3,2,1]=>85
[6,5,4,2,2,1]=>85
[6,5,4,3,1,1]=>85
[6,5,4,3,2]=>85
[6,5,2,2,2,2,1]=>88
[6,5,4,2,1,1,1]=>86
[6,6,2,2,2,2]=>88
[7,5,4,3,1]=>86
[2,2,2,2,2,2,2,2,2,2]=>120
[3,3,3,3,3,3,2]=>96
[4,4,3,3,3,3]=>90
[4,4,4,4,4]=>90
[5,5,5,5]=>90
[20]=>210
[10,10]=>120
[8,2,2,2,2,2,2]=>96
[8,6,4,2]=>90
[8,6,6]=>96
[10,6,4]=>100
[9,8,3]=>101
[6,6,6,2]=>90
[10,7,3]=>102
[9,7,4]=>98
[9,5,5,1]=>94
[6,5,4,3,2,1]=>91
[6,3,3,3,3,2,1]=>95
[6,5,3,2,2,2,1]=>93
[6,5,4,3,1,1,1]=>92
[7,6,2,2,2,2]=>95
[6,6,5,4]=>95
[3,3,3,3,3,3,3]=>105
[4,4,4,3,3,3]=>96
[21]=>231
[11,7,3]=>113
[5,4,2,2,2,2,2,2]=>101
[11,10]=>131
[13,4,4]=>123
[7,6,6,2]=>97
[4,4,4,4,3,2,1]=>102
[6,4,3,3,3,2,1]=>100
[6,5,4,2,2,2,1]=>99
[6,5,4,3,2,1,1]=>98
[4,4,4,4,3,3]=>103
[8,6,2,2,2,2]=>103
[22]=>253
[9,6,4,3]=>105
[8,7,7]=>113
[5,4,4,4,3,2,1]=>107
[6,5,3,3,3,2,1]=>106
[6,5,4,3,2,2,1]=>105
[15,2,2,2,2]=>152
[9,6,5,3]=>112
[8,6,5,3,1]=>108
[6,4,4,4,3,2,1]=>113
[6,5,4,3,3,2,1]=>112
[3,3,3,3,3,3,3,3]=>132
[4,4,4,4,4,4]=>120
[6,6,6,6]=>120
[24]=>300
[11,7,5,1]=>130
[9,7,5,3]=>120
[8,8,8]=>132
[17,7]=>188
[12,9,3]=>144
[5,5,5,4,3,2,1]=>120
[6,5,4,4,3,2,1]=>119
[7,6,6,6]=>127
[5,4,4,4,2,2,2,2]=>125
[13,12]=>181
[15,5,5]=>165
[9,7,5,3,1]=>125
[10,7,5,3]=>130
[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]=>165
[5,5,5,5,5]=>125
[12,10,3]=>155
[6,5,5,4,3,2,1]=>126
[6,6,4,3,3,2,2]=>127
[8,6,6,6]=>135
[9,7,5,4,1]=>132
[16,8,2]=>187
[6,6,5,4,3,2,1]=>133
[7,6,5,4,3,2]=>133
[3,3,3,3,3,3,3,3,3]=>162
[15,6,6]=>180
[7,6,5,4,3,2,1]=>140
[6,6,6,4,3,3]=>142
[4,3,3,3,3,3,3,3,3]=>166
[7,6,5,4,3,1,1,1]=>141
[10,7,6,4,1]=>150
[9,7,6,4,2]=>146
[10,8,5,4,1]=>151
[15,14]=>239
[7,6,5,4,3,2,1,1]=>148
[7,6,5,4,2,2,2,1]=>149
[10,8,6,4,1]=>159
[6,6,6,6,6]=>165
[15,15]=>255
[5,5,5,5,5,5]=>165
[6,6,6,6,3,3]=>159
[10,10,10]=>195
[9,7,5,5,3,1]=>159
[7,6,5,4,3,2,2,1]=>156
[7,6,5,3,3,3,2,1]=>157
[11,8,6,4,1]=>170
[10,8,6,4,2]=>165
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>255
[7,6,6,6,6]=>172
[7,6,5,4,3,3,2,1]=>164
[7,6,4,4,4,3,2,1]=>165
[11,8,6,5,1]=>178
[10,10,9,2]=>192
[14,9,8]=>211
[4,4,4,4,4,4,4,4]=>192
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>288
[7,6,5,4,4,3,2,1]=>172
[7,5,5,5,4,3,2,1]=>173
[16,16]=>288
[10,10,10,2]=>204
[16,8,4,2,2]=>218
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>291
[5,4,4,4,4,4,4,4]=>197
[7,6,5,5,4,3,2,1]=>180
[6,6,6,5,4,3,2,1]=>181
[22,7,4]=>306
[12,12,4,3,2]=>212
[4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>295
[7,6,6,5,4,3,2,1]=>188
[12,9,7,5,1]=>209
[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>280
[7,7,6,5,4,3,2,1]=>196
[13,9,7,5,1]=>222
[18,18]=>360
[24,12]=>390
[11,9,7,5,3,1]=>216
[11,8,7,5,4,1]=>214
[8,7,6,5,4,3,2,1]=>204
[8,7,7,7,7]=>218
[7,6,2,2,2,2,2,2,2,2,2,2,2,2]=>271
[7,6,6,6,6,6]=>223
[8,7,6,5,4,3,2,1,1]=>213
[8,7,6,5,4,3,2,2,1]=>222
[8,7,6,5,4,3,3,2,1]=>231
[10,10,10,10]=>280
[12,12,12,4]=>292
[8,7,6,5,4,4,3,2,1]=>240
[11,9,7,5,5,3]=>248
[4,4,4,4,4,4,4,4,4,4]=>280
[14,14,8,4]=>298
[7,6,6,6,2,2,2,2,2,2,2,2]=>271
[8,7,6,5,5,4,3,2,1]=>249
[9,9,9,9,3,3]=>273
[8,7,6,6,5,4,3,2,1]=>258
[10,10,10,5,5,2]=>273
[16,10,8,8]=>313
[26,9,7]=>447
[8,7,7,6,5,4,3,2,1]=>267
[8,8,7,6,5,4,3,2,1]=>276
[18,18,9]=>423
[9,8,7,6,5,4,3,2,1]=>285
[11,9,7,7,5,3,3]=>291
[48]=>1176
[7,6,6,6,6,6,6,6]=>343
[22,9,8,5,5]=>424
[6,6,6,6,6,6,6,3,3,2]=>351
[27,14,9]=>560
[17,14,13,8]=>449
[5,5,5,5,5,5,5,5,5,5,5]=>440
[27,20,8]=>660
[26,13,7,7,2]=>557
[31,12,10,4]=>683
[6,6,6,6,6,6,6,6,6,6]=>480
[5,5,5,5,5,5,5,5,5,5,5,5]=>510
[12,12,12,12,12]=>510
[12,12,12,12,11,4]=>524
[12,12,12,12,12,4]=>540
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>1091
[11,11,11,11,11,10]=>545
[11,11,11,11,11,11]=>561
[16,14,9,9,9,9]=>561
[8,8,8,8,8,8,8,8,4,2]=>575
[24,24,24]=>972
[16,16,16,16,8,4,2]=>753
[12,12,12,12,12,12,4,4]=>720
[22,20,20,12,8]=>915
[20,20,8,4,4,4,4,4,4,4,4,4]=>834
[33,32,9,9,5]=>1291
[18,18,18,18,18]=>1035
[18,18,18,18,9,9]=>963
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3]=>939
[56,17,11,10,5]=>1974
[33,26,23,12,9]=>1455
[22,22,22,10,10,9,4,4]=>1167
[22,22,22,10,10,10,4,4]=>1182
[12,12,12,12,12,12,12,12,4,3,2]=>1058
[24,24,24,24,14]=>1505
[76,22,9,6]=>3303
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>1610
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>1740
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>1560
[12,12,12,12,12,12,12,12,12,12]=>1320
[24,24,24,24,24]=>1740
[12,12,12,12,12,12,12,12,12,6,6,6,4,2]=>1464
[54,48,18,10,8]=>3069
[24,24,24,24,24,24]=>2160
[37,33,20,20,13,10,10,10,7]=>2389
[42,34,30,22,22,14,2]=>2907
[54,52,34,18,11,7]=>3976
[65,27,27,25,13,9,6,6]=>3735
[18,18,18,18,18,18,18,18,18,18]=>2520
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>3240
[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2]=>2353
[58,38,38,38,30]=>4747
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]=>3840
[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2]=>4428
[74,58,34,34,22,22,13,11,2]=>6939
[61,48,48,48,45,22,12,2]=>7452
[15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3]=>4805
[98,62,36,26,14,14,14,14,14,14,12,2]=>9432
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2]=>6840
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2]=>6878
[74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3]=>9034
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>11880
[64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6]=>8569
[70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3]=>9347
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2]=>9491
[170,92,36,28,27,24,20,14,13,10,8,8]=>22152
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3]=>11607
[145,83,62,44,44,42,19,16,16,10,8]=>20709
[98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8]=>18090
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>45360
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Description
The sum of the hook lengths of an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the sum of all hook lengths of a partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the sum of all hook lengths of a partition.
References
[1] Amdeberhan, T. Average on sum of hooks in a rectangle MathOverflow:273095
Code
def statistic(L):
return sum(L.hooks())
Created
Jun 27, 2017 at 09:02 by Christian Stump
Updated
Mar 11, 2024 at 11:26 by Martin Rubey
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