Identifier
- St000393: Binary words ⟶ ℤ
Values
=>
0=>1
1=>1
00=>2
01=>1
10=>2
11=>2
000=>3
001=>2
010=>2
011=>2
100=>3
101=>2
110=>3
111=>3
0000=>4
0001=>3
0010=>3
0011=>3
0100=>3
0101=>2
0110=>3
0111=>3
1000=>4
1001=>3
1010=>3
1011=>3
1100=>4
1101=>3
1110=>4
1111=>4
00000=>5
00001=>4
00010=>4
00011=>4
00100=>4
00101=>3
00110=>4
00111=>4
01000=>4
01001=>3
01010=>3
01011=>3
01100=>4
01101=>3
01110=>4
01111=>4
10000=>5
10001=>4
10010=>4
10011=>4
10100=>4
10101=>3
10110=>4
10111=>4
11000=>5
11001=>4
11010=>4
11011=>4
11100=>5
11101=>4
11110=>5
11111=>5
000000=>6
000001=>5
000010=>5
000011=>5
000100=>5
000101=>4
000110=>5
000111=>5
001000=>5
001001=>4
001010=>4
001011=>4
001100=>5
001101=>4
001110=>5
001111=>5
010000=>5
010001=>4
010010=>4
010011=>4
010100=>4
010101=>3
010110=>4
010111=>4
011000=>5
011001=>4
011010=>4
011011=>4
011100=>5
011101=>4
011110=>5
011111=>5
100000=>6
100001=>5
100010=>5
100011=>5
100100=>5
100101=>4
100110=>5
100111=>5
101000=>5
101001=>4
101010=>4
101011=>4
101100=>5
101101=>4
101110=>5
101111=>5
110000=>6
110001=>5
110010=>5
110011=>5
110100=>5
110101=>4
110110=>5
110111=>5
111000=>6
111001=>5
111010=>5
111011=>5
111100=>6
111101=>5
111110=>6
111111=>6
0000000=>7
0000001=>6
0000010=>6
0000011=>6
0000100=>6
0000101=>5
0000110=>6
0000111=>6
0001000=>6
0001001=>5
0001010=>5
0001011=>5
0001100=>6
0001101=>5
0001110=>6
0001111=>6
0010000=>6
0010001=>5
0010010=>5
0010011=>5
0010100=>5
0010101=>4
0010110=>5
0010111=>5
0011000=>6
0011001=>5
0011010=>5
0011011=>5
0011100=>6
0011101=>5
0011110=>6
0011111=>6
0100000=>6
0100001=>5
0100010=>5
0100011=>5
0100100=>5
0100101=>4
0100110=>5
0100111=>5
0101000=>5
0101001=>4
0101010=>4
0101011=>4
0101100=>5
0101101=>4
0101110=>5
0101111=>5
0110000=>6
0110001=>5
0110010=>5
0110011=>5
0110100=>5
0110101=>4
0110110=>5
0110111=>5
0111000=>6
0111001=>5
0111010=>5
0111011=>5
0111100=>6
0111101=>5
0111110=>6
0111111=>6
1000000=>7
1000001=>6
1000010=>6
1000011=>6
1000100=>6
1000101=>5
1000110=>6
1000111=>6
1001000=>6
1001001=>5
1001010=>5
1001011=>5
1001100=>6
1001101=>5
1001110=>6
1001111=>6
1010000=>6
1010001=>5
1010010=>5
1010011=>5
1010100=>5
1010101=>4
1010110=>5
1010111=>5
1011000=>6
1011001=>5
1011010=>5
1011011=>5
1011100=>6
1011101=>5
1011110=>6
1011111=>6
1100000=>7
1100001=>6
1100010=>6
1100011=>6
1100100=>6
1100101=>5
1100110=>6
1100111=>6
1101000=>6
1101001=>5
1101010=>5
1101011=>5
1101100=>6
1101101=>5
1101110=>6
1101111=>6
1110000=>7
1110001=>6
1110010=>6
1110011=>6
1110100=>6
1110101=>5
1110110=>6
1110111=>6
1111000=>7
1111001=>6
1111010=>6
1111011=>6
1111100=>7
1111101=>6
1111110=>7
1111111=>7
00000000=>8
00000001=>7
00000010=>7
00000011=>7
00000100=>7
00000101=>6
00000110=>7
00000111=>7
00001000=>7
00001001=>6
00001010=>6
00001011=>6
00001100=>7
00001101=>6
00001110=>7
00001111=>7
00010000=>7
00010001=>6
00010010=>6
00010011=>6
00010100=>6
00010101=>5
00010110=>6
00010111=>6
00011000=>7
00011001=>6
00011010=>6
00011011=>6
00011100=>7
00011101=>6
00011110=>7
00011111=>7
00100000=>7
00100001=>6
00100010=>6
00100011=>6
00100100=>6
00100101=>5
00100110=>6
00100111=>6
00101000=>6
00101001=>5
00101010=>5
00101011=>5
00101100=>6
00101101=>5
00101110=>6
00101111=>6
00110000=>7
00110001=>6
00110010=>6
00110011=>6
00110100=>6
00110101=>5
00110110=>6
00110111=>6
00111000=>7
00111001=>6
00111010=>6
00111011=>6
00111100=>7
00111101=>6
00111110=>7
00111111=>7
01000000=>7
01000001=>6
01000010=>6
01000011=>6
01000100=>6
01000101=>5
01000110=>6
01000111=>6
01001000=>6
01001001=>5
01001010=>5
01001011=>5
01001100=>6
01001101=>5
01001110=>6
01001111=>6
01010000=>6
01010001=>5
01010010=>5
01010011=>5
01010100=>5
01010101=>4
01010110=>5
01010111=>5
01011000=>6
01011001=>5
01011010=>5
01011011=>5
01011100=>6
01011101=>5
01011110=>6
01011111=>6
01100000=>7
01100001=>6
01100010=>6
01100011=>6
01100100=>6
01100101=>5
01100110=>6
01100111=>6
01101000=>6
01101001=>5
01101010=>5
01101011=>5
01101100=>6
01101101=>5
01101110=>6
01101111=>6
01110000=>7
01110001=>6
01110010=>6
01110011=>6
01110100=>6
01110101=>5
01110110=>6
01110111=>6
01111000=>7
01111001=>6
01111010=>6
01111011=>6
01111100=>7
01111101=>6
01111110=>7
01111111=>7
10000000=>8
10000001=>7
10000010=>7
10000011=>7
10000100=>7
10000101=>6
10000110=>7
10000111=>7
10001000=>7
10001001=>6
10001010=>6
10001011=>6
10001100=>7
10001101=>6
10001110=>7
10001111=>7
10010000=>7
10010001=>6
10010010=>6
10010011=>6
10010100=>6
10010101=>5
10010110=>6
10010111=>6
10011000=>7
10011001=>6
10011010=>6
10011011=>6
10011100=>7
10011101=>6
10011110=>7
10011111=>7
10100000=>7
10100001=>6
10100010=>6
10100011=>6
10100100=>6
10100101=>5
10100110=>6
10100111=>6
10101000=>6
10101001=>5
10101010=>5
10101011=>5
10101100=>6
10101101=>5
10101110=>6
10101111=>6
10110000=>7
10110001=>6
10110010=>6
10110011=>6
10110100=>6
10110101=>5
10110110=>6
10110111=>6
10111000=>7
10111001=>6
10111010=>6
10111011=>6
10111100=>7
10111101=>6
10111110=>7
10111111=>7
11000000=>8
11000001=>7
11000010=>7
11000011=>7
11000100=>7
11000101=>6
11000110=>7
11000111=>7
11001000=>7
11001001=>6
11001010=>6
11001011=>6
11001100=>7
11001101=>6
11001110=>7
11001111=>7
11010000=>7
11010001=>6
11010010=>6
11010011=>6
11010100=>6
11010101=>5
11010110=>6
11010111=>6
11011000=>7
11011001=>6
11011010=>6
11011011=>6
11011100=>7
11011101=>6
11011110=>7
11011111=>7
11100000=>8
11100001=>7
11100010=>7
11100011=>7
11100100=>7
11100101=>6
11100110=>7
11100111=>7
11101000=>7
11101001=>6
11101010=>6
11101011=>6
11101100=>7
11101101=>6
11101110=>7
11101111=>7
11110000=>8
11110001=>7
11110010=>7
11110011=>7
11110100=>7
11110101=>6
11110110=>7
11110111=>7
11111000=>8
11111001=>7
11111010=>7
11111011=>7
11111100=>8
11111101=>7
11111110=>8
11111111=>8
000000000=>9
000000001=>8
000000010=>8
000000011=>8
000000100=>8
000000101=>7
000000110=>8
000000111=>8
000001000=>8
000001001=>7
000001010=>7
000001011=>7
000001100=>8
000001101=>7
000001110=>8
000001111=>8
000010000=>8
000010001=>7
000010010=>7
000010011=>7
000010100=>7
000010101=>6
000010110=>7
000010111=>7
000011000=>8
000011001=>7
000011010=>7
000011011=>7
000011100=>8
000011101=>7
000011110=>8
000011111=>8
000100000=>8
000100001=>7
000100010=>7
000100011=>7
000100100=>7
000100101=>6
000100110=>7
000100111=>7
000101000=>7
000101001=>6
000101010=>6
000101011=>6
000101100=>7
000101101=>6
000101110=>7
000101111=>7
000110000=>8
000110001=>7
000110010=>7
000110011=>7
000110100=>7
000110101=>6
000110110=>7
000110111=>7
000111000=>8
000111001=>7
000111010=>7
000111011=>7
000111100=>8
000111101=>7
000111110=>8
000111111=>8
001000000=>8
001000001=>7
001000010=>7
001000011=>7
001000100=>7
001000101=>6
001000110=>7
001000111=>7
001001000=>7
001001001=>6
001001010=>6
001001011=>6
001001100=>7
001001101=>6
001001110=>7
001001111=>7
001010000=>7
001010001=>6
001010010=>6
001010011=>6
001010100=>6
001010101=>5
001010110=>6
001010111=>6
001011000=>7
001011001=>6
001011010=>6
001011011=>6
001011100=>7
001011101=>6
001011110=>7
001011111=>7
001100000=>8
001100001=>7
001100010=>7
001100011=>7
001100100=>7
001100101=>6
001100110=>7
001100111=>7
001101000=>7
001101001=>6
001101010=>6
001101011=>6
001101100=>7
001101101=>6
001101110=>7
001101111=>7
001110000=>8
001110001=>7
001110010=>7
001110011=>7
001110100=>7
001110101=>6
001110110=>7
001110111=>7
001111000=>8
001111001=>7
001111010=>7
001111011=>7
001111100=>8
001111101=>7
001111110=>8
001111111=>8
010000000=>8
010000001=>7
010000010=>7
010000011=>7
010000100=>7
010000101=>6
010000110=>7
010000111=>7
010001000=>7
010001001=>6
010001010=>6
010001011=>6
010001100=>7
010001101=>6
010001110=>7
010001111=>7
010010000=>7
010010001=>6
010010010=>6
010010011=>6
010010100=>6
010010101=>5
010010110=>6
010010111=>6
010011000=>7
010011001=>6
010011010=>6
010011011=>6
010011100=>7
010011101=>6
010011110=>7
010011111=>7
010100000=>7
010100001=>6
010100010=>6
010100011=>6
010100100=>6
010100101=>5
010100110=>6
010100111=>6
010101000=>6
010101001=>5
010101010=>5
010101011=>5
010101100=>6
010101101=>5
010101110=>6
010101111=>6
010110000=>7
010110001=>6
010110010=>6
010110011=>6
010110100=>6
010110101=>5
010110110=>6
010110111=>6
010111000=>7
010111001=>6
010111010=>6
010111011=>6
010111100=>7
010111101=>6
010111110=>7
010111111=>7
011000000=>8
011000001=>7
011000010=>7
011000011=>7
011000100=>7
011000101=>6
011000110=>7
011000111=>7
011001000=>7
011001001=>6
011001010=>6
011001011=>6
011001100=>7
011001101=>6
011001110=>7
011001111=>7
011010000=>7
011010001=>6
011010010=>6
011010011=>6
011010100=>6
011010101=>5
011010110=>6
011010111=>6
011011000=>7
011011001=>6
011011010=>6
011011011=>6
011011100=>7
011011101=>6
011011110=>7
011011111=>7
011100000=>8
011100001=>7
011100010=>7
011100011=>7
011100100=>7
011100101=>6
011100110=>7
011100111=>7
011101000=>7
011101001=>6
011101010=>6
011101011=>6
011101100=>7
011101101=>6
011101110=>7
011101111=>7
011110000=>8
011110001=>7
011110010=>7
011110011=>7
011110100=>7
011110101=>6
011110110=>7
011110111=>7
011111000=>8
011111001=>7
011111010=>7
011111011=>7
011111100=>8
011111101=>7
011111110=>8
011111111=>8
100000000=>9
100000001=>8
100000010=>8
100000011=>8
100000100=>8
100000101=>7
100000110=>8
100000111=>8
100001000=>8
100001001=>7
100001010=>7
100001011=>7
100001100=>8
100001101=>7
100001110=>8
100001111=>8
100010000=>8
100010001=>7
100010010=>7
100010011=>7
100010100=>7
100010101=>6
100010110=>7
100010111=>7
100011000=>8
100011001=>7
100011010=>7
100011011=>7
100011100=>8
100011101=>7
100011110=>8
100011111=>8
100100000=>8
100100001=>7
100100010=>7
100100011=>7
100100100=>7
100100101=>6
100100110=>7
100100111=>7
100101000=>7
100101001=>6
100101010=>6
100101011=>6
100101100=>7
100101101=>6
100101110=>7
100101111=>7
100110000=>8
100110001=>7
100110010=>7
100110011=>7
100110100=>7
100110101=>6
100110110=>7
100110111=>7
100111000=>8
100111001=>7
100111010=>7
100111011=>7
100111100=>8
100111101=>7
100111110=>8
100111111=>8
101000000=>8
101000001=>7
101000010=>7
101000011=>7
101000100=>7
101000101=>6
101000110=>7
101000111=>7
101001000=>7
101001001=>6
101001010=>6
101001011=>6
101001100=>7
101001101=>6
101001110=>7
101001111=>7
101010000=>7
101010001=>6
101010010=>6
101010011=>6
101010100=>6
101010101=>5
101010110=>6
101010111=>6
101011000=>7
101011001=>6
101011010=>6
101011011=>6
101011100=>7
101011101=>6
101011110=>7
101011111=>7
101100000=>8
101100001=>7
101100010=>7
101100011=>7
101100100=>7
101100101=>6
101100110=>7
101100111=>7
101101000=>7
101101001=>6
101101010=>6
101101011=>6
101101100=>7
101101101=>6
101101110=>7
101101111=>7
101110000=>8
101110001=>7
101110010=>7
101110011=>7
101110100=>7
101110101=>6
101110110=>7
101110111=>7
101111000=>8
101111001=>7
101111010=>7
101111011=>7
101111100=>8
101111101=>7
101111110=>8
101111111=>8
110000000=>9
110000001=>8
110000010=>8
110000011=>8
110000100=>8
110000101=>7
110000110=>8
110000111=>8
110001000=>8
110001001=>7
110001010=>7
110001011=>7
110001100=>8
110001101=>7
110001110=>8
110001111=>8
110010000=>8
110010001=>7
110010010=>7
110010011=>7
110010100=>7
110010101=>6
110010110=>7
110010111=>7
110011000=>8
110011001=>7
110011010=>7
110011011=>7
110011100=>8
110011101=>7
110011110=>8
110011111=>8
110100000=>8
110100001=>7
110100010=>7
110100011=>7
110100100=>7
110100101=>6
110100110=>7
110100111=>7
110101000=>7
110101001=>6
110101010=>6
110101011=>6
110101100=>7
110101101=>6
110101110=>7
110101111=>7
110110000=>8
110110001=>7
110110010=>7
110110011=>7
110110100=>7
110110101=>6
110110110=>7
110110111=>7
110111000=>8
110111001=>7
110111010=>7
110111011=>7
110111100=>8
110111101=>7
110111110=>8
110111111=>8
111000000=>9
111000001=>8
111000010=>8
111000011=>8
111000100=>8
111000101=>7
111000110=>8
111000111=>8
111001000=>8
111001001=>7
111001010=>7
111001011=>7
111001100=>8
111001101=>7
111001110=>8
111001111=>8
111010000=>8
111010001=>7
111010010=>7
111010011=>7
111010100=>7
111010101=>6
111010110=>7
111010111=>7
111011000=>8
111011001=>7
111011010=>7
111011011=>7
111011100=>8
111011101=>7
111011110=>8
111011111=>8
111100000=>9
111100001=>8
111100010=>8
111100011=>8
111100100=>8
111100101=>7
111100110=>8
111100111=>8
111101000=>8
111101001=>7
111101010=>7
111101011=>7
111101100=>8
111101101=>7
111101110=>8
111101111=>8
111110000=>9
111110001=>8
111110010=>8
111110011=>8
111110100=>8
111110101=>7
111110110=>8
111110111=>8
111111000=>9
111111001=>8
111111010=>8
111111011=>8
111111100=>9
111111101=>8
111111110=>9
111111111=>9
0000000001=>9
0010000001=>8
0010101101=>6
0010101011=>6
0010100111=>7
0010011101=>7
0010011011=>7
0010010111=>7
0010001111=>8
0001110101=>7
0001110011=>8
0001101101=>7
0001101011=>7
0001100111=>8
0001011101=>7
0001011011=>7
0001010111=>7
0001001111=>8
0000111101=>8
0000111011=>8
0000110111=>8
0000101111=>8
0000011111=>9
0000000000=>10
0000000110=>9
0000011000=>9
0000011110=>9
0000010010=>8
0001100000=>9
0001100110=>8
0001111000=>9
0001111110=>9
0001110010=>8
0001001000=>8
0001001110=>8
0001000010=>8
0001011010=>7
0010101010=>6
0010101000=>7
0010101100=>7
0010100100=>7
0010010100=>7
0001010100=>7
0010101110=>7
0010100000=>8
0010000100=>8
0000010100=>8
0000000010=>9
0000001110=>9
0000111110=>9
0000000100=>9
0000001010=>8
0000010110=>8
0000101110=>8
0001011110=>8
0001101110=>8
0001110110=>8
0001111010=>8
0001111100=>9
0000000101=>8
0000001101=>8
0000011101=>8
0001111101=>8
0000001001=>8
0000010101=>7
0000101101=>7
0010110001=>7
0001100001=>8
0001000001=>8
0000111111=>9
0001110100=>8
0001101100=>8
0010011100=>8
0001011100=>8
0000111100=>9
0001101010=>7
0010011010=>7
0000111010=>8
0010100110=>7
0010010110=>7
0001010110=>7
0000110110=>8
0010001110=>8
0001101001=>7
0000110001=>8
0000010001=>8
0000001100=>9
0000011001=>8
0000110011=>8
0000110100=>8
0000000011=>9
0000011011=>8
0001101111=>8
0000110101=>7
0010000010=>8
0001000011=>8
0010011110=>8
0001010000=>8
0001000100=>8
0001010101=>6
0001001011=>7
0001100011=>8
0001110111=>8
0010000000=>9
0000000111=>9
0000001111=>9
0001111111=>9
0000001011=>8
0000010111=>8
0001011111=>8
0001111001=>8
0000011010=>8
0000101010=>7
0000100101=>7
0010010001=>7
0010000101=>7
0010010101=>6
0010010011=>7
0000101011=>7
0001000111=>8
0000100111=>8
0010010010=>7
0001001010=>7
0001001001=>7
0001000101=>7
0000100011=>8
0000100100=>8
0000100010=>8
0010110000=>8
0000011100=>9
0000001000=>9
0000101100=>8
0010101111=>7
0000101000=>8
0010001000=>8
0001001100=>8
0001000110=>8
0001100100=>8
0001100010=>8
0000100110=>8
0000110010=>8
0010010000=>8
0001010010=>7
0001000000=>9
0001011001=>7
0001100101=>7
0001110001=>8
0010011001=>7
0010100101=>6
0010101001=>6
0010011111=>8
0000111001=>8
0010001101=>7
0001001101=>7
0001010001=>7
0001010011=>7
0001111011=>8
0010011000=>8
0001011000=>8
0000100000=>9
0010001011=>7
0010000111=>8
0000010011=>8
0010001100=>8
0010000110=>8
0000110000=>9
0000100001=>8
0010100011=>7
0010100001=>7
0000111000=>9
0001101000=>8
0000010000=>9
0000101001=>7
0010100010=>7
0010001001=>7
0010000011=>8
0010001010=>7
0001110000=>9
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 strictly increasing runs in a binary word.
Code
def statistic(w):
res = 1
last = w[0]
for e in w[1:]:
if e <= last:
res += 1
last = e
return res
Created
Feb 12, 2016 at 22:05 by Martin Rubey
Updated
Feb 12, 2016 at 22:05 by Martin Rubey
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