Identifier
- St000391: Binary words ⟶ ℤ
Values
0 => 0
1 => 1
00 => 0
01 => 2
10 => 1
11 => 3
000 => 0
001 => 3
010 => 2
011 => 5
100 => 1
101 => 4
110 => 3
111 => 6
0000 => 0
0001 => 4
0010 => 3
0011 => 7
0100 => 2
0101 => 6
0110 => 5
0111 => 9
1000 => 1
1001 => 5
1010 => 4
1011 => 8
1100 => 3
1101 => 7
1110 => 6
1111 => 10
00000 => 0
00001 => 5
00010 => 4
00011 => 9
00100 => 3
00101 => 8
00110 => 7
00111 => 12
01000 => 2
01001 => 7
01010 => 6
01011 => 11
01100 => 5
01101 => 10
01110 => 9
01111 => 14
10000 => 1
10001 => 6
10010 => 5
10011 => 10
10100 => 4
10101 => 9
10110 => 8
10111 => 13
11000 => 3
11001 => 8
11010 => 7
11011 => 12
11100 => 6
11101 => 11
11110 => 10
11111 => 15
000000 => 0
000001 => 6
000010 => 5
000011 => 11
000100 => 4
000101 => 10
000110 => 9
000111 => 15
001000 => 3
001001 => 9
001010 => 8
001011 => 14
001100 => 7
001101 => 13
001110 => 12
001111 => 18
010000 => 2
010001 => 8
010010 => 7
010011 => 13
010100 => 6
010101 => 12
010110 => 11
010111 => 17
011000 => 5
011001 => 11
011010 => 10
011011 => 16
011100 => 9
011101 => 15
011110 => 14
011111 => 20
100000 => 1
100001 => 7
100010 => 6
100011 => 12
100100 => 5
100101 => 11
100110 => 10
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Description
The sum of the positions of the ones in a binary word.
References
[1] Irregular triangle read by rows giving coefficients in expansion of Product_k=1..n (1 + x^k). OEIS:A053632
Code
def statistic(w):
return sum(i for (i, e) in enumerate(w, 1) if e == 1)
Created
Feb 12, 2016 at 21:50 by Martin Rubey
Updated
Feb 12, 2016 at 21:50 by Martin Rubey
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