Identifier
- St000389: Binary words ⟶ ℤ
Values
=>
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1=>1
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01=>1
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11=>0
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111000011001=>2
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011010100101=>4
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011010110001=>2
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011010111000=>2
011011000101=>2
011011000110=>0
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011011001010=>2
011011001100=>0
011011010001=>2
011011010010=>2
011011010100=>2
011011011000=>0
011011100001=>2
011011100010=>2
011011100100=>2
011011101000=>2
011011110000=>0
011100010101=>4
011100010110=>2
011100011001=>2
011100011100=>2
011100100101=>4
011100101001=>4
011100101010=>4
011100101100=>2
011100110001=>2
011100110100=>2
011101000101=>4
011101000110=>2
011101001001=>4
011101001100=>2
011101010001=>4
011101010010=>4
011101010100=>4
011101011000=>2
011101100001=>2
011101100100=>2
011101110000=>2
011110000101=>2
011110001001=>2
011110001010=>2
011110001100=>0
011110010001=>2
011110010100=>2
011110100001=>2
011110100010=>2
011110100100=>2
011110101000=>2
011110110000=>0
011111000001=>2
011111000100=>2
011111010000=>2
001111000110=>0
001111001010=>2
100111001100=>2
001111001100=>0
001011010110=>2
001111010010=>2
100111010100=>4
001111010100=>2
000111010110=>2
001011011010=>2
100111011000=>2
001111011000=>0
100011011100=>2
010011011100=>2
001011011100=>2
000111011100=>2
000011011110=>0
001101100110=>0
001101101010=>2
100101101100=>2
001101101100=>0
001011100110=>2
001111100010=>2
100111100100=>2
001111100100=>2
010011101010=>4
001011101010=>4
100111101000=>2
001111101000=>2
000111101010=>2
100011101100=>2
010011101100=>2
001011101100=>2
000111101100=>0
000011101110=>2
101001110100=>4
001001110110=>2
001101110010=>2
100101110100=>4
001101110100=>2
000101110110=>2
001011110010=>2
100111110000=>2
001111110000=>0
100011110100=>2
010011110100=>2
001011110100=>2
000111110100=>2
000011110110=>0
110001111000=>0
101001111000=>2
001001111010=>2
100101111000=>2
001101111000=>0
100011111000=>2
001011111000=>2
000011111010=>2
010001111100=>2
001001111100=>2
000101111100=>2
000011111100=>0
100101010101=>6
100101011001=>4
100101100101=>4
100101101001=>4
100101110001=>4
100110010101=>4
100110101001=>4
100111000101=>4
100111001001=>4
100111010001=>4
101001010101=>6
101001101001=>4
101010011001=>4
101010100101=>6
101010101001=>6
101010110001=>4
101011001001=>4
101011100001=>4
101100010101=>4
101100101001=>4
101101000101=>4
101101001001=>4
101101010001=>4
101110001001=>4
101110100001=>4
110001010101=>4
110001011001=>2
110001100101=>2
110001101001=>2
110001110001=>2
110010010101=>4
110010011001=>2
110010100101=>4
110010101001=>4
110010110001=>2
110011000101=>2
110011001001=>2
110011010001=>2
110011100001=>2
110100010101=>4
110100011001=>2
110100100101=>4
110100101001=>4
110100110001=>2
110101000101=>4
110101001001=>4
110101010001=>4
110101100001=>2
110110000101=>2
110110001001=>2
110110010001=>2
110110100001=>2
110111000001=>2
111000010101=>4
111000101001=>4
111001000101=>4
111001001001=>4
111001010001=>4
111010001001=>4
111010100001=>4
111100000101=>2
111100001001=>2
111100010001=>2
111100100001=>2
111101000001=>2
10110111100000=>1
10111011010000=>3
10111011100000=>3
10111100110000=>1
10111101001000=>3
10111101010000=>3
10111101100000=>1
10111110000100=>3
10111110001000=>3
10111110010000=>3
10111110100000=>3
10111111000000=>1
11001111100000=>1
11011110000010=>1
11101101000010=>3
11101110000010=>3
11110011000010=>1
11110100100010=>3
11110101000010=>3
11110110000010=>1
11111000001100=>1
11111000010010=>3
11111000100010=>3
11111001000010=>3
11111010000010=>3
11111100000010=>1
1011110111000000=>2
1011111010100000=>4
1011111011000000=>2
1011111100010000=>2
1011111100100000=>2
1011111101000000=>2
1011111110000000=>2
1111011100000010=>2
1111101010000010=>4
1111101100000010=>2
1111110001000010=>2
1111110010000010=>2
1111110100000010=>2
1111111000000010=>2
111111110000000010=>1
101111111100000000=>1
111111101000000010=>3
101111111010000000=>3
111111100100000010=>3
111111011000000010=>1
101111111001000000=>3
101111110110000000=>1
11111111100000000010=>2
10111111111000000000=>2
11111111010000000010=>2
10111111110100000000=>2
1111111111000000000010=>1
1011111111110000000000=>1
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Description
The number of runs of ones of odd length in a binary word.
References
[1] Triangle read by rows: T(n,k) is number of binary words of length n and having k runs of 0's of odd length, 0<=k<=ceil(n/2). (A run of 0's is a subsequence of consecutive 0's of maximal length). OEIS:A119473
Code
def statistic(w): if len(w) == 0: return 0 if w[0] == 1: c = Composition(w.delta())[::2] else: c = Composition(w.delta())[1::2] return len([1 for e in c if is_odd(e)])
Created
Feb 12, 2016 at 21:34 by Martin Rubey
Updated
Dec 30, 2017 at 22:04 by Martin Rubey
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