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
100111=>16
101000=>4
101001=>10
101010=>9
101011=>15
101100=>8
101101=>14
101110=>13
101111=>19
110000=>3
110001=>9
110010=>8
110011=>14
110100=>7
110101=>13
110110=>12
110111=>18
111000=>6
111001=>12
111010=>11
111011=>17
111100=>10
111101=>16
111110=>15
111111=>21
0000000=>0
0000001=>7
0000010=>6
0000011=>13
0000100=>5
0000101=>12
0000110=>11
0000111=>18
0001000=>4
0001001=>11
0001010=>10
0001011=>17
0001100=>9
0001101=>16
0001110=>15
0001111=>22
0010000=>3
0010001=>10
0010010=>9
0010011=>16
0010100=>8
0010101=>15
0010110=>14
0010111=>21
0011000=>7
0011001=>14
0011010=>13
0011011=>20
0011100=>12
0011101=>19
0011110=>18
0011111=>25
0100000=>2
0100001=>9
0100010=>8
0100011=>15
0100100=>7
0100101=>14
0100110=>13
0100111=>20
0101000=>6
0101001=>13
0101010=>12
0101011=>19
0101100=>11
0101101=>18
0101110=>17
0101111=>24
0110000=>5
0110001=>12
0110010=>11
0110011=>18
0110100=>10
0110101=>17
0110110=>16
0110111=>23
0111000=>9
0111001=>16
0111010=>15
0111011=>22
0111100=>14
0111101=>21
0111110=>20
0111111=>27
1000000=>1
1000001=>8
1000010=>7
1000011=>14
1000100=>6
1000101=>13
1000110=>12
1000111=>19
1001000=>5
1001001=>12
1001010=>11
1001011=>18
1001100=>10
1001101=>17
1001110=>16
1001111=>23
1010000=>4
1010001=>11
1010010=>10
1010011=>17
1010100=>9
1010101=>16
1010110=>15
1010111=>22
1011000=>8
1011001=>15
1011010=>14
1011011=>21
1011100=>13
1011101=>20
1011110=>19
1011111=>26
1100000=>3
1100001=>10
1100010=>9
1100011=>16
1100100=>8
1100101=>15
1100110=>14
1100111=>21
1101000=>7
1101001=>14
1101010=>13
1101011=>20
1101100=>12
1101101=>19
1101110=>18
1101111=>25
1110000=>6
1110001=>13
1110010=>12
1110011=>19
1110100=>11
1110101=>18
1110110=>17
1110111=>24
1111000=>10
1111001=>17
1111010=>16
1111011=>23
1111100=>15
1111101=>22
1111110=>21
1111111=>28
00000000=>0
00000001=>8
00000010=>7
00000011=>15
00000100=>6
00000101=>14
00000110=>13
00000111=>21
00001000=>5
00001001=>13
00001010=>12
00001011=>20
00001100=>11
00001101=>19
00001110=>18
00001111=>26
00010000=>4
00010001=>12
00010010=>11
00010011=>19
00010100=>10
00010101=>18
00010110=>17
00010111=>25
00011000=>9
00011001=>17
00011010=>16
00011011=>24
00011100=>15
00011101=>23
00011110=>22
00011111=>30
00100000=>3
00100001=>11
00100010=>10
00100011=>18
00100100=>9
00100101=>17
00100110=>16
00100111=>24
00101000=>8
00101001=>16
00101010=>15
00101011=>23
00101100=>14
00101101=>22
00101110=>21
00101111=>29
00110000=>7
00110001=>15
00110010=>14
00110011=>22
00110100=>13
00110101=>21
00110110=>20
00110111=>28
00111000=>12
00111001=>20
00111010=>19
00111011=>27
00111100=>18
00111101=>26
00111110=>25
00111111=>33
01000000=>2
01000001=>10
01000010=>9
01000011=>17
01000100=>8
01000101=>16
01000110=>15
01000111=>23
01001000=>7
01001001=>15
01001010=>14
01001011=>22
01001100=>13
01001101=>21
01001110=>20
01001111=>28
01010000=>6
01010001=>14
01010010=>13
01010011=>21
01010100=>12
01010101=>20
01010110=>19
01010111=>27
01011000=>11
01011001=>19
01011010=>18
01011011=>26
01011100=>17
01011101=>25
01011110=>24
01011111=>32
01100000=>5
01100001=>13
01100010=>12
01100011=>20
01100100=>11
01100101=>19
01100110=>18
01100111=>26
01101000=>10
01101001=>18
01101010=>17
01101011=>25
01101100=>16
01101101=>24
01101110=>23
01101111=>31
01110000=>9
01110001=>17
01110010=>16
01110011=>24
01110100=>15
01110101=>23
01110110=>22
01110111=>30
01111000=>14
01111001=>22
01111010=>21
01111011=>29
01111100=>20
01111101=>28
01111110=>27
01111111=>35
10000000=>1
10000001=>9
10000010=>8
10000011=>16
10000100=>7
10000101=>15
10000110=>14
10000111=>22
10001000=>6
10001001=>14
10001010=>13
10001011=>21
10001100=>12
10001101=>20
10001110=>19
10001111=>27
10010000=>5
10010001=>13
10010010=>12
10010011=>20
10010100=>11
10010101=>19
10010110=>18
10010111=>26
10011000=>10
10011001=>18
10011010=>17
10011011=>25
10011100=>16
10011101=>24
10011110=>23
10011111=>31
10100000=>4
10100001=>12
10100010=>11
10100011=>19
10100100=>10
10100101=>18
10100110=>17
10100111=>25
10101000=>9
10101001=>17
10101010=>16
10101011=>24
10101100=>15
10101101=>23
10101110=>22
10101111=>30
10110000=>8
10110001=>16
10110010=>15
10110011=>23
10110100=>14
10110101=>22
10110110=>21
10110111=>29
10111000=>13
10111001=>21
10111010=>20
10111011=>28
10111100=>19
10111101=>27
10111110=>26
10111111=>34
11000000=>3
11000001=>11
11000010=>10
11000011=>18
11000100=>9
11000101=>17
11000110=>16
11000111=>24
11001000=>8
11001001=>16
11001010=>15
11001011=>23
11001100=>14
11001101=>22
11001110=>21
11001111=>29
11010000=>7
11010001=>15
11010010=>14
11010011=>22
11010100=>13
11010101=>21
11010110=>20
11010111=>28
11011000=>12
11011001=>20
11011010=>19
11011011=>27
11011100=>18
11011101=>26
11011110=>25
11011111=>33
11100000=>6
11100001=>14
11100010=>13
11100011=>21
11100100=>12
11100101=>20
11100110=>19
11100111=>27
11101000=>11
11101001=>19
11101010=>18
11101011=>26
11101100=>17
11101101=>25
11101110=>24
11101111=>32
11110000=>10
11110001=>18
11110010=>17
11110011=>25
11110100=>16
11110101=>24
11110110=>23
11110111=>31
11111000=>15
11111001=>23
11111010=>22
11111011=>30
11111100=>21
11111101=>29
11111110=>28
11111111=>36
000000000=>0
000000001=>9
000000010=>8
000000011=>17
000000100=>7
000000101=>16
000000110=>15
000000111=>24
000001000=>6
000001001=>15
000001010=>14
000001011=>23
000001100=>13
000001101=>22
000001110=>21
000001111=>30
000010000=>5
000010001=>14
000010010=>13
000010011=>22
000010100=>12
000010101=>21
000010110=>20
000010111=>29
000011000=>11
000011001=>20
000011010=>19
000011011=>28
000011100=>18
000011101=>27
000011110=>26
000011111=>35
000100000=>4
000100001=>13
000100010=>12
000100011=>21
000100100=>11
000100101=>20
000100110=>19
000100111=>28
000101000=>10
000101001=>19
000101010=>18
000101011=>27
000101100=>17
000101101=>26
000101110=>25
000101111=>34
000110000=>9
000110001=>18
000110010=>17
000110011=>26
000110100=>16
000110101=>25
000110110=>24
000110111=>33
000111000=>15
000111001=>24
000111010=>23
000111011=>32
000111100=>22
000111101=>31
000111110=>30
000111111=>39
001000000=>3
001000001=>12
001000010=>11
001000011=>20
001000100=>10
001000101=>19
001000110=>18
001000111=>27
001001000=>9
001001001=>18
001001010=>17
001001011=>26
001001100=>16
001001101=>25
001001110=>24
001001111=>33
001010000=>8
001010001=>17
001010010=>16
001010011=>25
001010100=>15
001010101=>24
001010110=>23
001010111=>32
001011000=>14
001011001=>23
001011010=>22
001011011=>31
001011100=>21
001011101=>30
001011110=>29
001011111=>38
001100000=>7
001100001=>16
001100010=>15
001100011=>24
001100100=>14
001100101=>23
001100110=>22
001100111=>31
001101000=>13
001101001=>22
001101010=>21
001101011=>30
001101100=>20
001101101=>29
001101110=>28
001101111=>37
001110000=>12
001110001=>21
001110010=>20
001110011=>29
001110100=>19
001110101=>28
001110110=>27
001110111=>36
001111000=>18
001111001=>27
001111010=>26
001111011=>35
001111100=>25
001111101=>34
001111110=>33
001111111=>42
010000000=>2
010000001=>11
010000010=>10
010000011=>19
010000100=>9
010000101=>18
010000110=>17
010000111=>26
010001000=>8
010001001=>17
010001010=>16
010001011=>25
010001100=>15
010001101=>24
010001110=>23
010001111=>32
010010000=>7
010010001=>16
010010010=>15
010010011=>24
010010100=>14
010010101=>23
010010110=>22
010010111=>31
010011000=>13
010011001=>22
010011010=>21
010011011=>30
010011100=>20
010011101=>29
010011110=>28
010011111=>37
010100000=>6
010100001=>15
010100010=>14
010100011=>23
010100100=>13
010100101=>22
010100110=>21
010100111=>30
010101000=>12
010101001=>21
010101010=>20
010101011=>29
010101100=>19
010101101=>28
010101110=>27
010101111=>36
010110000=>11
010110001=>20
010110010=>19
010110011=>28
010110100=>18
010110101=>27
010110110=>26
010110111=>35
010111000=>17
010111001=>26
010111010=>25
010111011=>34
010111100=>24
010111101=>33
010111110=>32
010111111=>41
011000000=>5
011000001=>14
011000010=>13
011000011=>22
011000100=>12
011000101=>21
011000110=>20
011000111=>29
011001000=>11
011001001=>20
011001010=>19
011001011=>28
011001100=>18
011001101=>27
011001110=>26
011001111=>35
011010000=>10
011010001=>19
011010010=>18
011010011=>27
011010100=>17
011010101=>26
011010110=>25
011010111=>34
011011000=>16
011011001=>25
011011010=>24
011011011=>33
011011100=>23
011011101=>32
011011110=>31
011011111=>40
011100000=>9
011100001=>18
011100010=>17
011100011=>26
011100100=>16
011100101=>25
011100110=>24
011100111=>33
011101000=>15
011101001=>24
011101010=>23
011101011=>32
011101100=>22
011101101=>31
011101110=>30
011101111=>39
011110000=>14
011110001=>23
011110010=>22
011110011=>31
011110100=>21
011110101=>30
011110110=>29
011110111=>38
011111000=>20
011111001=>29
011111010=>28
011111011=>37
011111100=>27
011111101=>36
011111110=>35
011111111=>44
100000000=>1
100000001=>10
100000010=>9
100000011=>18
100000100=>8
100000101=>17
100000110=>16
100000111=>25
100001000=>7
100001001=>16
100001010=>15
100001011=>24
100001100=>14
100001101=>23
100001110=>22
100001111=>31
100010000=>6
100010001=>15
100010010=>14
100010011=>23
100010100=>13
100010101=>22
100010110=>21
100010111=>30
100011000=>12
100011001=>21
100011010=>20
100011011=>29
100011100=>19
100011101=>28
100011110=>27
100011111=>36
100100000=>5
100100001=>14
100100010=>13
100100011=>22
100100100=>12
100100101=>21
100100110=>20
100100111=>29
100101000=>11
100101001=>20
100101010=>19
100101011=>28
100101100=>18
100101101=>27
100101110=>26
100101111=>35
100110000=>10
100110001=>19
100110010=>18
100110011=>27
100110100=>17
100110101=>26
100110110=>25
100110111=>34
100111000=>16
100111001=>25
100111010=>24
100111011=>33
100111100=>23
100111101=>32
100111110=>31
100111111=>40
101000000=>4
101000001=>13
101000010=>12
101000011=>21
101000100=>11
101000101=>20
101000110=>19
101000111=>28
101001000=>10
101001001=>19
101001010=>18
101001011=>27
101001100=>17
101001101=>26
101001110=>25
101001111=>34
101010000=>9
101010001=>18
101010010=>17
101010011=>26
101010100=>16
101010101=>25
101010110=>24
101010111=>33
101011000=>15
101011001=>24
101011010=>23
101011011=>32
101011100=>22
101011101=>31
101011110=>30
101011111=>39
101100000=>8
101100001=>17
101100010=>16
101100011=>25
101100100=>15
101100101=>24
101100110=>23
101100111=>32
101101000=>14
101101001=>23
101101010=>22
101101011=>31
101101100=>21
101101101=>30
101101110=>29
101101111=>38
101110000=>13
101110001=>22
101110010=>21
101110011=>30
101110100=>20
101110101=>29
101110110=>28
101110111=>37
101111000=>19
101111001=>28
101111010=>27
101111011=>36
101111100=>26
101111101=>35
101111110=>34
101111111=>43
110000000=>3
110000001=>12
110000010=>11
110000011=>20
110000100=>10
110000101=>19
110000110=>18
110000111=>27
110001000=>9
110001001=>18
110001010=>17
110001011=>26
110001100=>16
110001101=>25
110001110=>24
110001111=>33
110010000=>8
110010001=>17
110010010=>16
110010011=>25
110010100=>15
110010101=>24
110010110=>23
110010111=>32
110011000=>14
110011001=>23
110011010=>22
110011011=>31
110011100=>21
110011101=>30
110011110=>29
110011111=>38
110100000=>7
110100001=>16
110100010=>15
110100011=>24
110100100=>14
110100101=>23
110100110=>22
110100111=>31
110101000=>13
110101001=>22
110101010=>21
110101011=>30
110101100=>20
110101101=>29
110101110=>28
110101111=>37
110110000=>12
110110001=>21
110110010=>20
110110011=>29
110110100=>19
110110101=>28
110110110=>27
110110111=>36
110111000=>18
110111001=>27
110111010=>26
110111011=>35
110111100=>25
110111101=>34
110111110=>33
110111111=>42
111000000=>6
111000001=>15
111000010=>14
111000011=>23
111000100=>13
111000101=>22
111000110=>21
111000111=>30
111001000=>12
111001001=>21
111001010=>20
111001011=>29
111001100=>19
111001101=>28
111001110=>27
111001111=>36
111010000=>11
111010001=>20
111010010=>19
111010011=>28
111010100=>18
111010101=>27
111010110=>26
111010111=>35
111011000=>17
111011001=>26
111011010=>25
111011011=>34
111011100=>24
111011101=>33
111011110=>32
111011111=>41
111100000=>10
111100001=>19
111100010=>18
111100011=>27
111100100=>17
111100101=>26
111100110=>25
111100111=>34
111101000=>16
111101001=>25
111101010=>24
111101011=>33
111101100=>23
111101101=>32
111101110=>31
111101111=>40
111110000=>15
111110001=>24
111110010=>23
111110011=>32
111110100=>22
111110101=>31
111110110=>30
111110111=>39
111111000=>21
111111001=>30
111111010=>29
111111011=>38
111111100=>28
111111101=>37
111111110=>36
111111111=>45
0000000001=>10
0010000001=>13
0010101101=>33
0010101011=>34
0010100111=>35
0010011101=>34
0010011011=>35
0010010111=>36
0010001111=>37
0001110101=>33
0001110011=>34
0001101101=>34
0001101011=>35
0001100111=>36
0001011101=>35
0001011011=>36
0001010111=>37
0001001111=>38
0000111101=>36
0000111011=>37
0000110111=>38
0000101111=>39
0000011111=>40
0000000000=>0
0000000110=>17
0000011000=>13
0000011110=>30
0000010010=>15
0001100000=>9
0001100110=>26
0001111000=>22
0001111110=>39
0001110010=>24
0001001000=>11
0001001110=>28
0001000010=>13
0001011010=>26
0010101010=>24
0010101000=>15
0010101100=>23
0010100100=>16
0010010100=>17
0001010100=>18
0010101110=>32
0010100000=>8
0010000100=>11
0000010100=>14
0000000010=>9
0000001110=>24
0000111110=>35
0000000100=>8
0000001010=>16
0000010110=>23
0000101110=>29
0001011110=>34
0001101110=>33
0001110110=>32
0001111010=>31
0001111100=>30
0000000101=>18
0000001101=>25
0000011101=>31
0001111101=>40
0000001001=>17
0000010101=>24
0000101101=>30
0010110001=>24
0001100001=>19
0001000001=>14
0000111111=>45
0001110100=>23
0001101100=>24
0010011100=>24
0001011100=>25
0000111100=>26
0001101010=>25
0010011010=>25
0000111010=>27
0010100110=>25
0010010110=>26
0001010110=>27
0000110110=>28
0010001110=>27
0001101001=>26
0000110001=>21
0000010001=>16
0000001100=>15
0000011001=>23
0000110011=>30
0000110100=>19
0000000011=>19
0000011011=>32
0001101111=>43
0000110101=>29
0010000010=>12
0001000011=>23
0010011110=>33
0001010000=>10
0001000100=>12
0001010101=>28
0001001011=>30
0001100011=>28
0001110111=>42
0010000000=>3
0000000111=>27
0000001111=>34
0001111111=>49
0000001011=>26
0000010111=>33
0001011111=>44
0001111001=>32
0000011010=>22
0000101010=>21
0000100101=>23
0010010001=>19
0010000101=>21
0010010101=>27
0010010011=>28
0000101011=>31
0001000111=>31
0000100111=>32
0010010010=>18
0001001010=>20
0001001001=>21
0001000101=>22
0000100011=>24
0000100100=>13
0000100010=>14
0010110000=>14
0000011100=>21
0000001000=>7
0000101100=>20
0010101111=>42
0000101000=>12
0010001000=>10
0001001100=>19
0001000110=>21
0001100100=>17
0001100010=>18
0000100110=>22
0000110010=>20
0010010000=>9
0001010010=>19
0001000000=>4
0001011001=>27
0001100101=>27
0001110001=>25
0010011001=>26
0010100101=>26
0010101001=>25
0010011111=>43
0000111001=>28
0010001101=>28
0001001101=>29
0001010001=>20
0001010011=>29
0001111011=>41
0010011000=>16
0001011000=>17
0000100000=>5
0010001011=>29
0010000111=>30
0000010011=>25
0010001100=>18
0010000110=>20
0000110000=>11
0000100001=>15
0010100011=>27
0010100001=>18
0000111000=>18
0001101000=>16
0000010000=>6
0000101001=>22
0010100010=>17
0010001001=>20
0010000011=>22
0010001010=>19
0001110000=>15
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
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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