***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000631 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The number of distinct palindromic decompositions of a binary word. A palindromic decomposition (paldec for short) of a word $w=a_1,\dots,a_n$ is any list of factors $p_1,\dots,p_k$ such that $w=p_1\dots p_k$ and each $p_i$ is a palindrome, i.e. coincides with itself read backwards. ----------------------------------------------------------------------------- References: [1] [[mo201205]] ----------------------------------------------------------------------------- Code: def statistic(w): return len(paldecs(w)) def paldecs(w): """ Return all distinct palindromic decompositions of w. sage: w = Word([1,1]) sage: paldecs(w) [[word: 1, word: 1], [word: 11]] sage: w = Word([1,0,1]) sage: paldecs(w) [[word: 1, word: 0, word: 1], [word: 101]] sage: w = Word([1,0,1,0,0,1]) sage: paldecs(w) [[word: 1, word: 0, word: 1, word: 0, word: 0, word: 1], [word: 1, word: 0, word: 1, word: 00, word: 1], [word: 1, word: 0, word: 1001], [word: 1, word: 010, word: 0, word: 1], [word: 101, word: 0, word: 0, word: 1], [word: 101, word: 00, word: 1]] sage: w = Word("referee") sage: paldecs(w) [[word: r, word: e, word: f, word: e, word: r, word: e, word: e], [word: r, word: e, word: f, word: e, word: r, word: ee], [word: r, word: e, word: f, word: ere, word: e], [word: r, word: efe, word: r, word: e, word: e], [word: r, word: efe, word: r, word: ee], [word: refer, word: e, word: e], [word: refer, word: ee]] """ if len(w) == 0: return [[]] P1 = w.palindrome_prefixes() result = [] for p1 in P1: l = len(p1) if l > 0: P2 = paldecs(w[l:]) for p2 in P2: result.append([p1] + p2) return result ----------------------------------------------------------------------------- Statistic values: 0 => 1 1 => 1 00 => 2 01 => 1 10 => 1 11 => 2 000 => 4 001 => 2 010 => 2 011 => 2 100 => 2 101 => 2 110 => 2 111 => 4 0000 => 8 0001 => 4 0010 => 3 0011 => 4 0100 => 3 0101 => 3 0110 => 3 0111 => 4 1000 => 4 1001 => 3 1010 => 3 1011 => 3 1100 => 4 1101 => 3 1110 => 4 1111 => 8 00000 => 16 00001 => 8 00010 => 6 00011 => 8 00100 => 6 00101 => 5 00110 => 5 00111 => 8 01000 => 6 01001 => 4 01010 => 5 01011 => 5 01100 => 5 01101 => 4 01110 => 5 01111 => 8 10000 => 8 10001 => 5 10010 => 4 10011 => 5 10100 => 5 10101 => 5 10110 => 4 10111 => 6 11000 => 8 11001 => 5 11010 => 5 11011 => 6 11100 => 8 11101 => 6 11110 => 8 11111 => 16 000000 => 32 000001 => 16 000010 => 12 000011 => 16 000100 => 11 000101 => 10 000110 => 10 000111 => 16 001000 => 11 001001 => 8 001010 => 8 001011 => 8 001100 => 10 001101 => 7 001110 => 9 001111 => 16 010000 => 12 010001 => 7 010010 => 7 010011 => 7 010100 => 8 010101 => 8 010110 => 6 010111 => 10 011000 => 10 011001 => 6 011010 => 6 011011 => 8 011100 => 9 011101 => 7 011110 => 9 011111 => 16 100000 => 16 100001 => 9 100010 => 7 100011 => 9 100100 => 8 100101 => 6 100110 => 6 100111 => 10 101000 => 10 101001 => 6 101010 => 8 101011 => 8 101100 => 7 101101 => 7 101110 => 7 101111 => 12 110000 => 16 110001 => 9 110010 => 7 110011 => 10 110100 => 8 110101 => 8 110110 => 8 110111 => 11 111000 => 16 111001 => 10 111010 => 10 111011 => 11 111100 => 16 111101 => 12 111110 => 16 111111 => 32 0000000 => 64 0000001 => 32 0000010 => 24 0000011 => 32 0000100 => 22 0000101 => 20 0000110 => 20 0000111 => 32 0001000 => 22 0001001 => 15 0001010 => 16 0001011 => 16 0001100 => 19 0001101 => 14 0001110 => 18 0001111 => 32 0010000 => 22 0010001 => 13 0010010 => 12 0010011 => 14 0010100 => 14 0010101 => 13 0010110 => 10 0010111 => 16 0011000 => 19 0011001 => 12 0011010 => 11 0011011 => 14 0011100 => 18 0011101 => 13 0011110 => 17 0011111 => 32 0100000 => 24 0100001 => 13 0100010 => 11 0100011 => 13 0100100 => 12 0100101 => 10 0100110 => 9 0100111 => 14 0101000 => 16 0101001 => 10 0101010 => 13 0101011 => 13 0101100 => 11 0101101 => 10 0101110 => 11 0101111 => 20 0110000 => 20 0110001 => 11 0110010 => 9 0110011 => 12 0110100 => 10 0110101 => 10 0110110 => 11 0110111 => 15 0111000 => 18 0111001 => 11 0111010 => 11 0111011 => 13 0111100 => 17 0111101 => 13 0111110 => 17 0111111 => 32 1000000 => 32 1000001 => 17 1000010 => 13 1000011 => 17 1000100 => 13 1000101 => 11 1000110 => 11 1000111 => 18 1001000 => 15 1001001 => 11 1001010 => 10 1001011 => 10 1001100 => 12 1001101 => 9 1001110 => 11 1001111 => 20 1010000 => 20 1010001 => 11 1010010 => 10 1010011 => 11 1010100 => 13 1010101 => 13 1010110 => 10 1010111 => 16 1011000 => 14 1011001 => 9 1011010 => 10 1011011 => 12 1011100 => 13 1011101 => 11 1011110 => 13 1011111 => 24 1100000 => 32 1100001 => 17 1100010 => 13 1100011 => 18 1100100 => 14 1100101 => 11 1100110 => 12 1100111 => 19 1101000 => 16 1101001 => 10 1101010 => 13 1101011 => 14 1101100 => 14 1101101 => 12 1101110 => 13 1101111 => 22 1110000 => 32 1110001 => 18 1110010 => 14 1110011 => 19 1110100 => 16 1110101 => 16 1110110 => 15 1110111 => 22 1111000 => 32 1111001 => 20 1111010 => 20 1111011 => 22 1111100 => 32 1111101 => 24 1111110 => 32 1111111 => 64 00000000 => 128 00000001 => 64 00000010 => 48 00000011 => 64 00000100 => 44 00000101 => 40 00000110 => 40 00000111 => 64 00001000 => 43 00001001 => 30 00001010 => 32 00001011 => 32 00001100 => 38 00001101 => 28 00001110 => 36 00001111 => 64 00010000 => 43 00010001 => 26 00010010 => 23 00010011 => 26 00010100 => 27 00010101 => 26 00010110 => 20 00010111 => 32 00011000 => 38 00011001 => 23 00011010 => 22 00011011 => 28 00011100 => 35 00011101 => 26 00011110 => 34 00011111 => 64 00100000 => 44 00100001 => 24 00100010 => 20 00100011 => 24 00100100 => 23 00100101 => 18 00100110 => 17 00100111 => 28 00101000 => 27 00101001 => 17 00101010 => 21 00101011 => 21 00101100 => 18 00101101 => 17 00101110 => 18 00101111 => 32 00110000 => 38 00110001 => 21 00110010 => 17 00110011 => 24 00110100 => 18 00110101 => 18 00110110 => 19 00110111 => 26 00111000 => 35 00111001 => 22 00111010 => 21 00111011 => 24 00111100 => 34 00111101 => 25 00111110 => 33 00111111 => 64 01000000 => 48 01000001 => 25 01000010 => 20 01000011 => 25 01000100 => 20 01000101 => 17 01000110 => 16 01000111 => 26 01001000 => 23 01001001 => 16 01001010 => 16 01001011 => 17 01001100 => 17 01001101 => 13 01001110 => 16 01001111 => 28 01010000 => 32 01010001 => 18 01010010 => 16 01010011 => 18 01010100 => 21 01010101 => 21 01010110 => 16 01010111 => 26 01011000 => 22 01011001 => 14 01011010 => 16 01011011 => 18 01011100 => 21 01011101 => 17 01011110 => 21 01011111 => 40 01100000 => 40 01100001 => 21 01100010 => 16 01100011 => 22 01100100 => 17 01100101 => 14 01100110 => 16 01100111 => 23 01101000 => 20 01101001 => 13 01101010 => 16 01101011 => 17 01101100 => 19 01101101 => 16 01101110 => 17 01101111 => 30 01110000 => 36 01110001 => 20 01110010 => 16 01110011 => 21 01110100 => 18 01110101 => 18 01110110 => 17 01110111 => 26 01111000 => 34 01111001 => 21 01111010 => 21 01111011 => 24 01111100 => 33 01111101 => 25 01111110 => 33 01111111 => 64 10000000 => 64 10000001 => 33 10000010 => 25 10000011 => 33 10000100 => 24 10000101 => 21 10000110 => 21 10000111 => 34 10001000 => 26 10001001 => 17 10001010 => 18 10001011 => 18 10001100 => 21 10001101 => 16 10001110 => 20 10001111 => 36 10010000 => 30 10010001 => 17 10010010 => 16 10010011 => 19 10010100 => 17 10010101 => 16 10010110 => 13 10010111 => 20 10011000 => 23 10011001 => 16 10011010 => 14 10011011 => 17 10011100 => 22 10011101 => 16 10011110 => 21 10011111 => 40 10100000 => 40 10100001 => 21 10100010 => 17 10100011 => 21 10100100 => 18 10100101 => 16 10100110 => 14 10100111 => 22 10101000 => 26 10101001 => 16 10101010 => 21 10101011 => 21 10101100 => 18 10101101 => 16 10101110 => 18 10101111 => 32 10110000 => 28 10110001 => 16 10110010 => 13 10110011 => 17 10110100 => 17 10110101 => 16 10110110 => 16 10110111 => 23 10111000 => 26 10111001 => 16 10111010 => 17 10111011 => 20 10111100 => 25 10111101 => 20 10111110 => 25 10111111 => 48 11000000 => 64 11000001 => 33 11000010 => 25 11000011 => 34 11000100 => 24 11000101 => 21 11000110 => 22 11000111 => 35 11001000 => 26 11001001 => 19 11001010 => 18 11001011 => 18 11001100 => 24 11001101 => 17 11001110 => 21 11001111 => 38 11010000 => 32 11010001 => 18 11010010 => 17 11010011 => 18 11010100 => 21 11010101 => 21 11010110 => 17 11010111 => 27 11011000 => 28 11011001 => 17 11011010 => 18 11011011 => 23 11011100 => 24 11011101 => 20 11011110 => 24 11011111 => 44 11100000 => 64 11100001 => 34 11100010 => 26 11100011 => 35 11100100 => 28 11100101 => 22 11100110 => 23 11100111 => 38 11101000 => 32 11101001 => 20 11101010 => 26 11101011 => 27 11101100 => 26 11101101 => 23 11101110 => 26 11101111 => 43 11110000 => 64 11110001 => 36 11110010 => 28 11110011 => 38 11110100 => 32 11110101 => 32 11110110 => 30 11110111 => 43 11111000 => 64 11111001 => 40 11111010 => 40 11111011 => 44 11111100 => 64 11111101 => 48 11111110 => 64 11111111 => 128 000000000 => 256 000000001 => 128 000000010 => 96 000000011 => 128 000000100 => 88 000000101 => 80 000000110 => 80 000000111 => 128 000001000 => 86 000001001 => 60 000001010 => 64 000001011 => 64 000001100 => 76 000001101 => 56 000001110 => 72 000001111 => 128 000010000 => 86 000010001 => 51 000010010 => 46 000010011 => 52 000010100 => 54 000010101 => 52 000010110 => 40 000010111 => 64 000011000 => 75 000011001 => 46 000011010 => 44 000011011 => 56 000011100 => 70 000011101 => 52 000011110 => 68 000011111 => 128 000100000 => 86 000100001 => 47 000100010 => 39 000100011 => 48 000100100 => 43 000100101 => 34 000100110 => 32 000100111 => 52 000101000 => 54 000101001 => 33 000101010 => 42 000101011 => 42 000101100 => 36 000101101 => 34 000101110 => 36 000101111 => 64 000110000 => 75 000110001 => 42 000110010 => 33 000110011 => 46 000110100 => 36 000110101 => 36 000110110 => 38 000110111 => 52 000111000 => 70 000111001 => 43 000111010 => 42 000111011 => 48 000111100 => 67 000111101 => 50 000111110 => 66 000111111 => 128 001000000 => 88 001000001 => 46 001000010 => 36 001000011 => 46 001000100 => 37 001000101 => 31 001000110 => 30 001000111 => 48 001001000 => 43 001001001 => 31 001001010 => 29 001001011 => 30 001001100 => 33 001001101 => 25 001001110 => 31 001001111 => 56 001010000 => 54 001010001 => 30 001010010 => 27 001010011 => 31 001010100 => 35 001010101 => 34 001010110 => 26 001010111 => 42 001011000 => 36 001011001 => 23 001011010 => 26 001011011 => 30 001011100 => 34 001011101 => 28 001011110 => 34 001011111 => 64 001100000 => 76 001100001 => 40 001100010 => 31 001100011 => 42 001100100 => 33 001100101 => 27 001100110 => 30 001100111 => 46 001101000 => 36 001101001 => 23 001101010 => 29 001101011 => 31 001101100 => 34 001101101 => 28 001101110 => 30 001101111 => 52 001110000 => 70 001110001 => 39 001110010 => 31 001110011 => 42 001110100 => 34 001110101 => 34 001110110 => 32 001110111 => 48 001111000 => 67 001111001 => 42 001111010 => 41 001111011 => 46 001111100 => 66 001111101 => 49 001111110 => 65 001111111 => 128 010000000 => 96 010000001 => 49 010000010 => 38 010000011 => 49 010000100 => 36 010000101 => 32 010000110 => 31 010000111 => 50 010001000 => 39 010001001 => 26 010001010 => 27 010001011 => 28 010001100 => 31 010001101 => 23 010001110 => 29 010001111 => 52 010010000 => 46 010010001 => 26 010010010 => 26 010010011 => 28 010010100 => 27 010010101 => 26 010010110 => 21 010010111 => 34 010011000 => 33 010011001 => 22 010011010 => 20 010011011 => 25 010011100 => 31 010011101 => 23 010011110 => 30 010011111 => 56 010100000 => 64 010100001 => 34 010100010 => 27 010100011 => 34 010100100 => 29 010100101 => 25 010100110 => 23 010100111 => 36 010101000 => 42 010101001 => 26 010101010 => 34 010101011 => 34 010101100 => 29 010101101 => 26 010101110 => 29 010101111 => 52 010110000 => 44 010110001 => 25 010110010 => 20 010110011 => 27 010110100 => 26 010110101 => 25 010110110 => 24 010110111 => 34 010111000 => 42 010111001 => 26 010111010 => 28 010111011 => 31 010111100 => 41 010111101 => 32 010111110 => 41 010111111 => 80 011000000 => 80 011000001 => 41 011000010 => 31 011000011 => 42 011000100 => 30 011000101 => 26 011000110 => 28 011000111 => 43 011001000 => 32 011001001 => 23 011001010 => 23 011001011 => 23 011001100 => 30 011001101 => 22 011001110 => 26 011001111 => 46 011010000 => 40 011010001 => 23 011010010 => 21 011010011 => 23 011010100 => 26 011010101 => 26 011010110 => 22 011010111 => 33 011011000 => 38 011011001 => 23 011011010 => 24 011011011 => 31 011011100 => 32 011011101 => 26 011011110 => 32 011011111 => 60 011100000 => 72 011100001 => 38 011100010 => 29 011100011 => 39 011100100 => 31 011100101 => 25 011100110 => 26 011100111 => 42 011101000 => 36 011101001 => 23 011101010 => 29 011101011 => 30 011101100 => 30 011101101 => 26 011101110 => 31 011101111 => 51 011110000 => 68 011110001 => 38 011110010 => 30 011110011 => 40 011110100 => 34 011110101 => 34 011110110 => 32 011110111 => 47 011111000 => 66 011111001 => 41 011111010 => 41 011111011 => 46 011111100 => 65 011111101 => 49 011111110 => 65 011111111 => 128 100000000 => 128 100000001 => 65 100000010 => 49 100000011 => 65 100000100 => 46 100000101 => 41 100000110 => 41 100000111 => 66 100001000 => 47 100001001 => 32 100001010 => 34 100001011 => 34 100001100 => 40 100001101 => 30 100001110 => 38 100001111 => 68 100010000 => 51 100010001 => 31 100010010 => 26 100010011 => 30 100010100 => 30 100010101 => 29 100010110 => 23 100010111 => 36 100011000 => 42 100011001 => 26 100011010 => 25 100011011 => 31 100011100 => 39 100011101 => 29 100011110 => 38 100011111 => 72 100100000 => 60 100100001 => 32 100100010 => 26 100100011 => 32 100100100 => 31 100100101 => 24 100100110 => 23 100100111 => 38 100101000 => 33 100101001 => 22 100101010 => 26 100101011 => 26 100101100 => 23 100101101 => 21 100101110 => 23 100101111 => 40 100110000 => 46 100110001 => 26 100110010 => 22 100110011 => 30 100110100 => 23 100110101 => 23 100110110 => 23 100110111 => 32 100111000 => 43 100111001 => 28 100111010 => 26 100111011 => 30 100111100 => 42 100111101 => 31 100111110 => 41 100111111 => 80 101000000 => 80 101000001 => 41 101000010 => 32 101000011 => 41 101000100 => 31 101000101 => 28 101000110 => 26 101000111 => 42 101001000 => 34 101001001 => 24 101001010 => 25 101001011 => 26 101001100 => 27 101001101 => 20 101001110 => 25 101001111 => 44 101010000 => 52 101010001 => 29 101010010 => 26 101010011 => 29 101010100 => 34 101010101 => 34 101010110 => 26 101010111 => 42 101011000 => 36 101011001 => 23 101011010 => 25 101011011 => 29 101011100 => 34 101011101 => 27 101011110 => 34 101011111 => 64 101100000 => 56 101100001 => 30 101100010 => 23 101100011 => 31 101100100 => 25 101100101 => 20 101100110 => 22 101100111 => 33 101101000 => 34 101101001 => 21 101101010 => 26 101101011 => 27 101101100 => 28 101101101 => 26 101101110 => 26 101101111 => 46 101110000 => 52 101110001 => 29 101110010 => 23 101110011 => 31 101110100 => 28 101110101 => 27 101110110 => 26 101110111 => 39 101111000 => 50 101111001 => 31 101111010 => 32 101111011 => 36 101111100 => 49 101111101 => 38 101111110 => 49 101111111 => 96 110000000 => 128 110000001 => 65 110000010 => 49 110000011 => 66 110000100 => 46 110000101 => 41 110000110 => 42 110000111 => 67 110001000 => 48 110001001 => 32 110001010 => 34 110001011 => 34 110001100 => 42 110001101 => 31 110001110 => 39 110001111 => 70 110010000 => 52 110010001 => 30 110010010 => 28 110010011 => 34 110010100 => 31 110010101 => 29 110010110 => 23 110010111 => 36 110011000 => 46 110011001 => 30 110011010 => 27 110011011 => 33 110011100 => 42 110011101 => 31 110011110 => 40 110011111 => 76 110100000 => 64 110100001 => 34 110100010 => 28 110100011 => 34 110100100 => 30 110100101 => 26 110100110 => 23 110100111 => 36 110101000 => 42 110101001 => 26 110101010 => 34 110101011 => 35 110101100 => 31 110101101 => 27 110101110 => 30 110101111 => 54 110110000 => 56 110110001 => 31 110110010 => 25 110110011 => 33 110110100 => 30 110110101 => 29 110110110 => 31 110110111 => 43 110111000 => 48 110111001 => 30 110111010 => 31 110111011 => 37 110111100 => 46 110111101 => 36 110111110 => 46 110111111 => 88 111000000 => 128 111000001 => 66 111000010 => 50 111000011 => 67 111000100 => 48 111000101 => 42 111000110 => 43 111000111 => 70 111001000 => 52 111001001 => 38 111001010 => 36 111001011 => 36 111001100 => 46 111001101 => 33 111001110 => 42 111001111 => 75 111010000 => 64 111010001 => 36 111010010 => 34 111010011 => 36 111010100 => 42 111010101 => 42 111010110 => 33 111010111 => 54 111011000 => 52 111011001 => 32 111011010 => 34 111011011 => 43 111011100 => 48 111011101 => 39 111011110 => 47 111011111 => 86 111100000 => 128 111100001 => 68 111100010 => 52 111100011 => 70 111100100 => 56 111100101 => 44 111100110 => 46 111100111 => 75 111101000 => 64 111101001 => 40 111101010 => 52 111101011 => 54 111101100 => 52 111101101 => 46 111101110 => 51 111101111 => 86 111110000 => 128 111110001 => 72 111110010 => 56 111110011 => 76 111110100 => 64 111110101 => 64 111110110 => 60 111110111 => 86 111111000 => 128 111111001 => 80 111111010 => 80 111111011 => 88 111111100 => 128 111111101 => 96 111111110 => 128 111111111 => 256 0000000001 => 256 0010000001 => 90 0010101101 => 42 0010101011 => 55 0010100111 => 62 0010011101 => 45 0010011011 => 48 0010010111 => 60 0010001111 => 96 0001110101 => 68 0001110011 => 82 0001101101 => 56 0001101011 => 62 0001100111 => 88 0001011101 => 56 0001011011 => 60 0001010111 => 84 0001001111 => 104 0000111101 => 100 0000111011 => 96 0000110111 => 104 0000101111 => 128 0000011111 => 256 0000000000 => 512 0000000110 => 160 0000011000 => 150 0000011110 => 136 0000010010 => 92 0001100000 => 150 0001100110 => 58 0001111000 => 134 0001111110 => 130 0001110010 => 61 0001001000 => 82 0001001110 => 58 0001000010 => 71 0001011010 => 52 0010101010 => 55 0010101000 => 69 0010101100 => 47 0010100100 => 49 0010010100 => 49 0001010100 => 69 0010101110 => 47 0010100000 => 108 0010000100 => 67 0000010100 => 108 0000000010 => 192 0000001110 => 144 0000111110 => 132 0000000100 => 176 0000001010 => 128 0000010110 => 80 0000101110 => 72 0001011110 => 68 0001101110 => 60 0001110110 => 64 0001111010 => 82 0001111100 => 131 0000000101 => 160 0000001101 => 112 0000011101 => 104 0001111101 => 98 0000001001 => 120 0000010101 => 104 0000101101 => 68 0010110001 => 41 0001100001 => 79 0001000001 => 90 0000111111 => 256 0001110100 => 68 0001101100 => 67 0010011100 => 61 0001011100 => 68 0000111100 => 134 0001101010 => 58 0010011010 => 39 0000111010 => 84 0010100110 => 39 0010010110 => 38 0001010110 => 52 0000110110 => 76 0010001110 => 54 0001101001 => 46 0000110001 => 83 0000010001 => 102 0000001100 => 152 0000011001 => 92 0000110011 => 92 0000110100 => 72 0000000011 => 256 0000011011 => 112 0001101111 => 104 0000110101 => 72 0010000010 => 69 0001000011 => 90 0010011110 => 59 0001010000 => 107 0001000100 => 72 0001010101 => 68 0001001011 => 57 0001100011 => 84 0001110111 => 96 0010000000 => 176 0000000111 => 256 0000001111 => 256 0001111111 => 256 0000001011 => 128 0000010111 => 128 0001011111 => 128 0001111001 => 83 0000011010 => 88 0000101010 => 84 0000100101 => 68 0010010001 => 49 0010000101 => 58 0010010101 => 47 0010010011 => 54 0000101011 => 84 0001000111 => 96 0000100111 => 104 0010010010 => 47 0001001010 => 55 0001001001 => 58 0001000101 => 61 0000100011 => 94 0000100100 => 86 0000100010 => 77 0010110000 => 72 0000011100 => 140 0000001000 => 172 0000101100 => 72 0010101111 => 84 0000101000 => 107 0010001000 => 72 0001001100 => 62 0001000110 => 59 0001100100 => 64 0001100010 => 61 0000100110 => 64 0000110010 => 66 0010010000 => 86 0001010010 => 53 0001000000 => 172 0001011001 => 46 0001100101 => 52 0001110001 => 78 0010011001 => 43 0010100101 => 43 0010101001 => 43 0010011111 => 112 0000111001 => 86 0010001101 => 43 0001001101 => 47 0001010001 => 60 0001010011 => 60 0001111011 => 92 0010011000 => 64 0001011000 => 72 0000100000 => 171 0010001011 => 51 0010000111 => 92 0000010011 => 104 0010001100 => 57 0010000110 => 57 0000110000 => 150 0000100001 => 94 0010100011 => 57 0010100001 => 57 0000111000 => 139 0001101000 => 72 0000010000 => 171 0000101001 => 66 0010100010 => 46 0010001001 => 48 0010000011 => 90 0010001010 => 50 0001110000 => 139 ----------------------------------------------------------------------------- Created: Oct 16, 2016 at 21:12 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 16, 2016 at 21:12 by Martin Rubey