Identifier
- St000691: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>0
01=>1
10=>1
11=>0
000=>0
001=>1
010=>2
011=>1
100=>1
101=>2
110=>1
111=>0
0000=>0
0001=>1
0010=>2
0011=>1
0100=>2
0101=>3
0110=>2
0111=>1
1000=>1
1001=>2
1010=>3
1011=>2
1100=>1
1101=>2
1110=>1
1111=>0
00000=>0
00001=>1
00010=>2
00011=>1
00100=>2
00101=>3
00110=>2
00111=>1
01000=>2
01001=>3
01010=>4
01011=>3
01100=>2
01101=>3
01110=>2
01111=>1
10000=>1
10001=>2
10010=>3
10011=>2
10100=>3
10101=>4
10110=>3
10111=>2
11000=>1
11001=>2
11010=>3
11011=>2
11100=>1
11101=>2
11110=>1
11111=>0
000000=>0
000001=>1
000010=>2
000011=>1
000100=>2
000101=>3
000110=>2
000111=>1
001000=>2
001001=>3
001010=>4
001011=>3
001100=>2
001101=>3
001110=>2
001111=>1
010000=>2
010001=>3
010010=>4
010011=>3
010100=>4
010101=>5
010110=>4
010111=>3
011000=>2
011001=>3
011010=>4
011011=>3
011100=>2
011101=>3
011110=>2
011111=>1
100000=>1
100001=>2
100010=>3
100011=>2
100100=>3
100101=>4
100110=>3
100111=>2
101000=>3
101001=>4
101010=>5
101011=>4
101100=>3
101101=>4
101110=>3
101111=>2
110000=>1
110001=>2
110010=>3
110011=>2
110100=>3
110101=>4
110110=>3
110111=>2
111000=>1
111001=>2
111010=>3
111011=>2
111100=>1
111101=>2
111110=>1
111111=>0
0000000=>0
0000001=>1
0000010=>2
0000011=>1
0000100=>2
0000101=>3
0000110=>2
0000111=>1
0001000=>2
0001001=>3
0001010=>4
0001011=>3
0001100=>2
0001101=>3
0001110=>2
0001111=>1
0010000=>2
0010001=>3
0010010=>4
0010011=>3
0010100=>4
0010101=>5
0010110=>4
0010111=>3
0011000=>2
0011001=>3
0011010=>4
0011011=>3
0011100=>2
0011101=>3
0011110=>2
0011111=>1
0100000=>2
0100001=>3
0100010=>4
0100011=>3
0100100=>4
0100101=>5
0100110=>4
0100111=>3
0101000=>4
0101001=>5
0101010=>6
0101011=>5
0101100=>4
0101101=>5
0101110=>4
0101111=>3
0110000=>2
0110001=>3
0110010=>4
0110011=>3
0110100=>4
0110101=>5
0110110=>4
0110111=>3
0111000=>2
0111001=>3
0111010=>4
0111011=>3
0111100=>2
0111101=>3
0111110=>2
0111111=>1
1000000=>1
1000001=>2
1000010=>3
1000011=>2
1000100=>3
1000101=>4
1000110=>3
1000111=>2
1001000=>3
1001001=>4
1001010=>5
1001011=>4
1001100=>3
1001101=>4
1001110=>3
1001111=>2
1010000=>3
1010001=>4
1010010=>5
1010011=>4
1010100=>5
1010101=>6
1010110=>5
1010111=>4
1011000=>3
1011001=>4
1011010=>5
1011011=>4
1011100=>3
1011101=>4
1011110=>3
1011111=>2
1100000=>1
1100001=>2
1100010=>3
1100011=>2
1100100=>3
1100101=>4
1100110=>3
1100111=>2
1101000=>3
1101001=>4
1101010=>5
1101011=>4
1101100=>3
1101101=>4
1101110=>3
1101111=>2
1110000=>1
1110001=>2
1110010=>3
1110011=>2
1110100=>3
1110101=>4
1110110=>3
1110111=>2
1111000=>1
1111001=>2
1111010=>3
1111011=>2
1111100=>1
1111101=>2
1111110=>1
1111111=>0
00000000=>0
00000001=>1
00000010=>2
00000011=>1
00000100=>2
00000101=>3
00000110=>2
00000111=>1
00001000=>2
00001001=>3
00001010=>4
00001011=>3
00001100=>2
00001101=>3
00001110=>2
00001111=>1
00010000=>2
00010001=>3
00010010=>4
00010011=>3
00010100=>4
00010101=>5
00010110=>4
00010111=>3
00011000=>2
00011001=>3
00011010=>4
00011011=>3
00011100=>2
00011101=>3
00011110=>2
00011111=>1
00100000=>2
00100001=>3
00100010=>4
00100011=>3
00100100=>4
00100101=>5
00100110=>4
00100111=>3
00101000=>4
00101001=>5
00101010=>6
00101011=>5
00101100=>4
00101101=>5
00101110=>4
00101111=>3
00110000=>2
00110001=>3
00110010=>4
00110011=>3
00110100=>4
00110101=>5
00110110=>4
00110111=>3
00111000=>2
00111001=>3
00111010=>4
00111011=>3
00111100=>2
00111101=>3
00111110=>2
00111111=>1
01000000=>2
01000001=>3
01000010=>4
01000011=>3
01000100=>4
01000101=>5
01000110=>4
01000111=>3
01001000=>4
01001001=>5
01001010=>6
01001011=>5
01001100=>4
01001101=>5
01001110=>4
01001111=>3
01010000=>4
01010001=>5
01010010=>6
01010011=>5
01010100=>6
01010101=>7
01010110=>6
01010111=>5
01011000=>4
01011001=>5
01011010=>6
01011011=>5
01011100=>4
01011101=>5
01011110=>4
01011111=>3
01100000=>2
01100001=>3
01100010=>4
01100011=>3
01100100=>4
01100101=>5
01100110=>4
01100111=>3
01101000=>4
01101001=>5
01101010=>6
01101011=>5
01101100=>4
01101101=>5
01101110=>4
01101111=>3
01110000=>2
01110001=>3
01110010=>4
01110011=>3
01110100=>4
01110101=>5
01110110=>4
01110111=>3
01111000=>2
01111001=>3
01111010=>4
01111011=>3
01111100=>2
01111101=>3
01111110=>2
01111111=>1
10000000=>1
10000001=>2
10000010=>3
10000011=>2
10000100=>3
10000101=>4
10000110=>3
10000111=>2
10001000=>3
10001001=>4
10001010=>5
10001011=>4
10001100=>3
10001101=>4
10001110=>3
10001111=>2
10010000=>3
10010001=>4
10010010=>5
10010011=>4
10010100=>5
10010101=>6
10010110=>5
10010111=>4
10011000=>3
10011001=>4
10011010=>5
10011011=>4
10011100=>3
10011101=>4
10011110=>3
10011111=>2
10100000=>3
10100001=>4
10100010=>5
10100011=>4
10100100=>5
10100101=>6
10100110=>5
10100111=>4
10101000=>5
10101001=>6
10101010=>7
10101011=>6
10101100=>5
10101101=>6
10101110=>5
10101111=>4
10110000=>3
10110001=>4
10110010=>5
10110011=>4
10110100=>5
10110101=>6
10110110=>5
10110111=>4
10111000=>3
10111001=>4
10111010=>5
10111011=>4
10111100=>3
10111101=>4
10111110=>3
10111111=>2
11000000=>1
11000001=>2
11000010=>3
11000011=>2
11000100=>3
11000101=>4
11000110=>3
11000111=>2
11001000=>3
11001001=>4
11001010=>5
11001011=>4
11001100=>3
11001101=>4
11001110=>3
11001111=>2
11010000=>3
11010001=>4
11010010=>5
11010011=>4
11010100=>5
11010101=>6
11010110=>5
11010111=>4
11011000=>3
11011001=>4
11011010=>5
11011011=>4
11011100=>3
11011101=>4
11011110=>3
11011111=>2
11100000=>1
11100001=>2
11100010=>3
11100011=>2
11100100=>3
11100101=>4
11100110=>3
11100111=>2
11101000=>3
11101001=>4
11101010=>5
11101011=>4
11101100=>3
11101101=>4
11101110=>3
11101111=>2
11110000=>1
11110001=>2
11110010=>3
11110011=>2
11110100=>3
11110101=>4
11110110=>3
11110111=>2
11111000=>1
11111001=>2
11111010=>3
11111011=>2
11111100=>1
11111101=>2
11111110=>1
11111111=>0
000000000=>0
000000001=>1
000000010=>2
000000011=>1
000000100=>2
000000101=>3
000000110=>2
000000111=>1
000001000=>2
000001001=>3
000001010=>4
000001011=>3
000001100=>2
000001101=>3
000001110=>2
000001111=>1
000010000=>2
000010001=>3
000010010=>4
000010011=>3
000010100=>4
000010101=>5
000010110=>4
000010111=>3
000011000=>2
000011001=>3
000011010=>4
000011011=>3
000011100=>2
000011101=>3
000011110=>2
000011111=>1
000100000=>2
000100001=>3
000100010=>4
000100011=>3
000100100=>4
000100101=>5
000100110=>4
000100111=>3
000101000=>4
000101001=>5
000101010=>6
000101011=>5
000101100=>4
000101101=>5
000101110=>4
000101111=>3
000110000=>2
000110001=>3
000110010=>4
000110011=>3
000110100=>4
000110101=>5
000110110=>4
000110111=>3
000111000=>2
000111001=>3
000111010=>4
000111011=>3
000111100=>2
000111101=>3
000111110=>2
000111111=>1
001000000=>2
001000001=>3
001000010=>4
001000011=>3
001000100=>4
001000101=>5
001000110=>4
001000111=>3
001001000=>4
001001001=>5
001001010=>6
001001011=>5
001001100=>4
001001101=>5
001001110=>4
001001111=>3
001010000=>4
001010001=>5
001010010=>6
001010011=>5
001010100=>6
001010101=>7
001010110=>6
001010111=>5
001011000=>4
001011001=>5
001011010=>6
001011011=>5
001011100=>4
001011101=>5
001011110=>4
001011111=>3
001100000=>2
001100001=>3
001100010=>4
001100011=>3
001100100=>4
001100101=>5
001100110=>4
001100111=>3
001101000=>4
001101001=>5
001101010=>6
001101011=>5
001101100=>4
001101101=>5
001101110=>4
001101111=>3
001110000=>2
001110001=>3
001110010=>4
001110011=>3
001110100=>4
001110101=>5
001110110=>4
001110111=>3
001111000=>2
001111001=>3
001111010=>4
001111011=>3
001111100=>2
001111101=>3
001111110=>2
001111111=>1
010000000=>2
010000001=>3
010000010=>4
010000011=>3
010000100=>4
010000101=>5
010000110=>4
010000111=>3
010001000=>4
010001001=>5
010001010=>6
010001011=>5
010001100=>4
010001101=>5
010001110=>4
010001111=>3
010010000=>4
010010001=>5
010010010=>6
010010011=>5
010010100=>6
010010101=>7
010010110=>6
010010111=>5
010011000=>4
010011001=>5
010011010=>6
010011011=>5
010011100=>4
010011101=>5
010011110=>4
010011111=>3
010100000=>4
010100001=>5
010100010=>6
010100011=>5
010100100=>6
010100101=>7
010100110=>6
010100111=>5
010101000=>6
010101001=>7
010101010=>8
010101011=>7
010101100=>6
010101101=>7
010101110=>6
010101111=>5
010110000=>4
010110001=>5
010110010=>6
010110011=>5
010110100=>6
010110101=>7
010110110=>6
010110111=>5
010111000=>4
010111001=>5
010111010=>6
010111011=>5
010111100=>4
010111101=>5
010111110=>4
010111111=>3
011000000=>2
011000001=>3
011000010=>4
011000011=>3
011000100=>4
011000101=>5
011000110=>4
011000111=>3
011001000=>4
011001001=>5
011001010=>6
011001011=>5
011001100=>4
011001101=>5
011001110=>4
011001111=>3
011010000=>4
011010001=>5
011010010=>6
011010011=>5
011010100=>6
011010101=>7
011010110=>6
011010111=>5
011011000=>4
011011001=>5
011011010=>6
011011011=>5
011011100=>4
011011101=>5
011011110=>4
011011111=>3
011100000=>2
011100001=>3
011100010=>4
011100011=>3
011100100=>4
011100101=>5
011100110=>4
011100111=>3
011101000=>4
011101001=>5
011101010=>6
011101011=>5
011101100=>4
011101101=>5
011101110=>4
011101111=>3
011110000=>2
011110001=>3
011110010=>4
011110011=>3
011110100=>4
011110101=>5
011110110=>4
011110111=>3
011111000=>2
011111001=>3
011111010=>4
011111011=>3
011111100=>2
011111101=>3
011111110=>2
011111111=>1
100000000=>1
100000001=>2
100000010=>3
100000011=>2
100000100=>3
100000101=>4
100000110=>3
100000111=>2
100001000=>3
100001001=>4
100001010=>5
100001011=>4
100001100=>3
100001101=>4
100001110=>3
100001111=>2
100010000=>3
100010001=>4
100010010=>5
100010011=>4
100010100=>5
100010101=>6
100010110=>5
100010111=>4
100011000=>3
100011001=>4
100011010=>5
100011011=>4
100011100=>3
100011101=>4
100011110=>3
100011111=>2
100100000=>3
100100001=>4
100100010=>5
100100011=>4
100100100=>5
100100101=>6
100100110=>5
100100111=>4
100101000=>5
100101001=>6
100101010=>7
100101011=>6
100101100=>5
100101101=>6
100101110=>5
100101111=>4
100110000=>3
100110001=>4
100110010=>5
100110011=>4
100110100=>5
100110101=>6
100110110=>5
100110111=>4
100111000=>3
100111001=>4
100111010=>5
100111011=>4
100111100=>3
100111101=>4
100111110=>3
100111111=>2
101000000=>3
101000001=>4
101000010=>5
101000011=>4
101000100=>5
101000101=>6
101000110=>5
101000111=>4
101001000=>5
101001001=>6
101001010=>7
101001011=>6
101001100=>5
101001101=>6
101001110=>5
101001111=>4
101010000=>5
101010001=>6
101010010=>7
101010011=>6
101010100=>7
101010101=>8
101010110=>7
101010111=>6
101011000=>5
101011001=>6
101011010=>7
101011011=>6
101011100=>5
101011101=>6
101011110=>5
101011111=>4
101100000=>3
101100001=>4
101100010=>5
101100011=>4
101100100=>5
101100101=>6
101100110=>5
101100111=>4
101101000=>5
101101001=>6
101101010=>7
101101011=>6
101101100=>5
101101101=>6
101101110=>5
101101111=>4
101110000=>3
101110001=>4
101110010=>5
101110011=>4
101110100=>5
101110101=>6
101110110=>5
101110111=>4
101111000=>3
101111001=>4
101111010=>5
101111011=>4
101111100=>3
101111101=>4
101111110=>3
101111111=>2
110000000=>1
110000001=>2
110000010=>3
110000011=>2
110000100=>3
110000101=>4
110000110=>3
110000111=>2
110001000=>3
110001001=>4
110001010=>5
110001011=>4
110001100=>3
110001101=>4
110001110=>3
110001111=>2
110010000=>3
110010001=>4
110010010=>5
110010011=>4
110010100=>5
110010101=>6
110010110=>5
110010111=>4
110011000=>3
110011001=>4
110011010=>5
110011011=>4
110011100=>3
110011101=>4
110011110=>3
110011111=>2
110100000=>3
110100001=>4
110100010=>5
110100011=>4
110100100=>5
110100101=>6
110100110=>5
110100111=>4
110101000=>5
110101001=>6
110101010=>7
110101011=>6
110101100=>5
110101101=>6
110101110=>5
110101111=>4
110110000=>3
110110001=>4
110110010=>5
110110011=>4
110110100=>5
110110101=>6
110110110=>5
110110111=>4
110111000=>3
110111001=>4
110111010=>5
110111011=>4
110111100=>3
110111101=>4
110111110=>3
110111111=>2
111000000=>1
111000001=>2
111000010=>3
111000011=>2
111000100=>3
111000101=>4
111000110=>3
111000111=>2
111001000=>3
111001001=>4
111001010=>5
111001011=>4
111001100=>3
111001101=>4
111001110=>3
111001111=>2
111010000=>3
111010001=>4
111010010=>5
111010011=>4
111010100=>5
111010101=>6
111010110=>5
111010111=>4
111011000=>3
111011001=>4
111011010=>5
111011011=>4
111011100=>3
111011101=>4
111011110=>3
111011111=>2
111100000=>1
111100001=>2
111100010=>3
111100011=>2
111100100=>3
111100101=>4
111100110=>3
111100111=>2
111101000=>3
111101001=>4
111101010=>5
111101011=>4
111101100=>3
111101101=>4
111101110=>3
111101111=>2
111110000=>1
111110001=>2
111110010=>3
111110011=>2
111110100=>3
111110101=>4
111110110=>3
111110111=>2
111111000=>1
111111001=>2
111111010=>3
111111011=>2
111111100=>1
111111101=>2
111111110=>1
111111111=>0
0000000001=>1
0010000001=>3
0010101101=>7
0010101011=>7
0010100111=>5
0010011101=>5
0010011011=>5
0010010111=>5
0010001111=>3
0001110101=>5
0001110011=>3
0001101101=>5
0001101011=>5
0001100111=>3
0001011101=>5
0001011011=>5
0001010111=>5
0001001111=>3
0000111101=>3
0000111011=>3
0000110111=>3
0000101111=>3
0000011111=>1
0000000000=>0
0000000110=>2
0000011000=>2
0000011110=>2
0000010010=>4
0001100000=>2
0001100110=>4
0001111000=>2
0001111110=>2
0001110010=>4
0001001000=>4
0001001110=>4
0001000010=>4
0001011010=>6
0010101010=>8
0010101000=>6
0010101100=>6
0010100100=>6
0010010100=>6
0001010100=>6
0010101110=>6
0010100000=>4
0010000100=>4
0000010100=>4
0000000010=>2
0000001110=>2
0000111110=>2
0000000100=>2
0000001010=>4
0000010110=>4
0000101110=>4
0001011110=>4
0001101110=>4
0001110110=>4
0001111010=>4
0001111100=>2
0000000101=>3
0000001101=>3
0000011101=>3
0001111101=>3
0000001001=>3
0000010101=>5
0000101101=>5
0010110001=>5
0001100001=>3
0001000001=>3
0000111111=>1
0001110100=>4
0001101100=>4
0010011100=>4
0001011100=>4
0000111100=>2
0001101010=>6
0010011010=>6
0000111010=>4
0010100110=>6
0010010110=>6
0001010110=>6
0000110110=>4
0010001110=>4
0001101001=>5
0000110001=>3
0000010001=>3
0000001100=>2
0000011001=>3
0000110011=>3
0000110100=>4
0000000011=>1
0000011011=>3
0001101111=>3
0000110101=>5
0010000010=>4
0001000011=>3
0010011110=>4
0001010000=>4
0001000100=>4
0001010101=>7
0001001011=>5
0001100011=>3
0001110111=>3
0010000000=>2
0000000111=>1
0000001111=>1
0001111111=>1
0000001011=>3
0000010111=>3
0001011111=>3
0001111001=>3
0000011010=>4
0000101010=>6
0000100101=>5
0010010001=>5
0010000101=>5
0010010101=>7
0010010011=>5
0000101011=>5
0001000111=>3
0000100111=>3
0010010010=>6
0001001010=>6
0001001001=>5
0001000101=>5
0000100011=>3
0000100100=>4
0000100010=>4
0010110000=>4
0000011100=>2
0000001000=>2
0000101100=>4
0010101111=>5
0000101000=>4
0010001000=>4
0001001100=>4
0001000110=>4
0001100100=>4
0001100010=>4
0000100110=>4
0000110010=>4
0010010000=>4
0001010010=>6
0001000000=>2
0001011001=>5
0001100101=>5
0001110001=>3
0010011001=>5
0010100101=>7
0010101001=>7
0010011111=>3
0000111001=>3
0010001101=>5
0001001101=>5
0001010001=>5
0001010011=>5
0001111011=>3
0010011000=>4
0001011000=>4
0000100000=>2
0010001011=>5
0010000111=>3
0000010011=>3
0010001100=>4
0010000110=>4
0000110000=>2
0000100001=>3
0010100011=>5
0010100001=>5
0000111000=>2
0001101000=>4
0000010000=>2
0000101001=>5
0010100010=>6
0010001001=>5
0010000011=>3
0010001010=>6
0001110000=>2
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 number of changes of a binary word.
This is the number of indices $i$ such that $w_i \neq w_{i+1}$.
This is the number of indices $i$ such that $w_i \neq w_{i+1}$.
Code
def statistic(w): return sum( 1 for i in range(len(w)-Integer(1)) if w[i] != w[i+1] )
Created
Jan 26, 2017 at 12:24 by Christian Stump
Updated
Jan 26, 2017 at 12:24 by Christian Stump
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