The 12 tables below list all A140108(n) solutions for n=1..12; each row represents one of the ways to divide an n X n square into sub-squares (where a "way" is defined as a distinct set of numbers of n X n, (n-1) X (n-1), ..., 2 X 2, and 1 X 1 squares). ================================================== Ways to divide a 1 X 1 square into sub-squares: 1 === 1 A140108(1) = 1 ================================================== Ways to divide a 2 X 2 square into sub-squares: 2 1 === === 0 4 1 0 A140108(2) = 2 ================================================== Ways to divide a 3 X 3 square into sub-squares: 3 2 1 === === === 0 0 9 0 1 5 1 0 0 A140108(3) = 3 ================================================== Ways to divide a 4 X 4 square into sub-squares: 4 3 2 1 === === === === 0 0 0 16 0 0 1 12 0 0 2 8 0 0 3 4 0 0 4 0 0 1 0 7 1 0 0 0 A140108(4) = 7 ================================================== Ways to divide a 5 X 5 square into sub-squares: 5 4 3 2 1 === === === === === 0 0 0 0 25 0 0 0 1 21 0 0 0 2 17 0 0 0 3 13 0 0 0 4 9 0 0 1 0 16 0 0 1 1 12 0 0 1 2 8 0 0 1 3 4 0 1 0 0 9 1 0 0 0 0 A140108(5) = 11 ================================================== Ways to divide a 6 X 6 square into sub-squares: 6 5 4 3 2 1 === === === === === === 0 0 0 0 0 36 0 0 0 0 1 32 0 0 0 0 2 28 0 0 0 0 3 24 0 0 0 0 4 20 0 0 0 0 5 16 0 0 0 0 6 12 0 0 0 0 7 8 0 0 0 0 8 4 0 0 0 0 9 0 0 0 0 1 0 27 0 0 0 1 1 23 0 0 0 1 2 19 0 0 0 1 3 15 0 0 0 1 4 11 0 0 0 1 5 7 0 0 0 2 0 18 0 0 0 2 1 14 0 0 0 2 2 10 0 0 0 2 3 6 0 0 0 3 0 9 0 0 0 3 1 5 0 0 0 4 0 0 0 0 1 0 0 20 0 0 1 0 1 16 0 0 1 0 2 12 0 0 1 0 3 8 0 0 1 0 4 4 0 0 1 0 5 0 0 1 0 0 0 11 1 0 0 0 0 0 A140108(6) = 31 ================================================== Ways to divide a 7 X 7 square into sub-squares: 7 6 5 4 3 2 1 === === === === === === === 0 0 0 0 0 0 49 0 0 0 0 0 1 45 0 0 0 0 0 2 41 0 0 0 0 0 3 37 0 0 0 0 0 4 33 0 0 0 0 0 5 29 0 0 0 0 0 6 25 0 0 0 0 0 7 21 0 0 0 0 0 8 17 0 0 0 0 0 9 13 0 0 0 0 1 0 40 0 0 0 0 1 1 36 0 0 0 0 1 2 32 0 0 0 0 1 3 28 0 0 0 0 1 4 24 0 0 0 0 1 5 20 0 0 0 0 1 6 16 0 0 0 0 1 7 12 0 0 0 0 1 8 8 0 0 0 0 2 0 31 0 0 0 0 2 1 27 0 0 0 0 2 2 23 0 0 0 0 2 3 19 0 0 0 0 2 4 15 0 0 0 0 2 5 11 0 0 0 0 2 6 7 0 0 0 0 2 7 3 0 0 0 0 3 0 22 0 0 0 0 3 1 18 0 0 0 0 3 2 14 0 0 0 0 3 3 10 0 0 0 0 3 4 6 0 0 0 0 4 0 13 0 0 0 1 0 0 33 0 0 0 1 0 1 29 0 0 0 1 0 2 25 0 0 0 1 0 3 21 0 0 0 1 0 4 17 0 0 0 1 0 5 13 0 0 0 1 1 0 24 0 0 0 1 1 1 20 0 0 0 1 1 2 16 0 0 0 1 1 3 12 0 0 0 1 1 4 8 0 0 0 1 2 0 15 0 0 0 1 2 1 11 0 0 0 1 2 2 7 0 0 0 1 2 3 3 0 0 0 1 3 0 6 0 0 1 0 0 0 24 0 0 1 0 0 1 20 0 0 1 0 0 2 16 0 0 1 0 0 3 12 0 0 1 0 0 4 8 0 0 1 0 0 5 4 0 1 0 0 0 0 13 1 0 0 0 0 0 0 A140108(7) = 57 ================================================== Ways to divide an 8 X 8 square into sub-squares: 8 7 6 5 4 3 2 1 === === === === === === === === 0 0 0 0 0 0 0 64 0 0 0 0 0 0 1 60 0 0 0 0 0 0 2 56 0 0 0 0 0 0 3 52 0 0 0 0 0 0 4 48 0 0 0 0 0 0 5 44 0 0 0 0 0 0 6 40 0 0 0 0 0 0 7 36 0 0 0 0 0 0 8 32 0 0 0 0 0 0 9 28 0 0 0 0 0 0 10 24 0 0 0 0 0 0 11 20 0 0 0 0 0 0 12 16 0 0 0 0 0 0 13 12 0 0 0 0 0 0 14 8 0 0 0 0 0 0 15 4 0 0 0 0 0 0 16 0 0 0 0 0 0 1 0 55 0 0 0 0 0 1 1 51 0 0 0 0 0 1 2 47 0 0 0 0 0 1 3 43 0 0 0 0 0 1 4 39 0 0 0 0 0 1 5 35 0 0 0 0 0 1 6 31 0 0 0 0 0 1 7 27 0 0 0 0 0 1 8 23 0 0 0 0 0 1 9 19 0 0 0 0 0 1 10 15 0 0 0 0 0 1 11 11 0 0 0 0 0 1 12 7 0 0 0 0 0 2 0 46 0 0 0 0 0 2 1 42 0 0 0 0 0 2 2 38 0 0 0 0 0 2 3 34 0 0 0 0 0 2 4 30 0 0 0 0 0 2 5 26 0 0 0 0 0 2 6 22 0 0 0 0 0 2 7 18 0 0 0 0 0 2 8 14 0 0 0 0 0 2 9 10 0 0 0 0 0 2 10 6 0 0 0 0 0 3 0 37 0 0 0 0 0 3 1 33 0 0 0 0 0 3 2 29 0 0 0 0 0 3 3 25 0 0 0 0 0 3 4 21 0 0 0 0 0 3 5 17 0 0 0 0 0 3 6 13 0 0 0 0 0 3 7 9 0 0 0 0 0 3 8 5 0 0 0 0 0 4 0 28 0 0 0 0 0 4 1 24 0 0 0 0 0 4 2 20 0 0 0 0 0 4 3 16 0 0 0 0 0 4 4 12 0 0 0 0 0 4 5 8 0 0 0 0 0 4 6 4 0 0 0 0 0 4 7 0 0 0 0 0 1 0 0 48 0 0 0 0 1 0 1 44 0 0 0 0 1 0 2 40 0 0 0 0 1 0 3 36 0 0 0 0 1 0 4 32 0 0 0 0 1 0 5 28 0 0 0 0 1 0 6 24 0 0 0 0 1 0 7 20 0 0 0 0 1 0 8 16 0 0 0 0 1 0 9 12 0 0 0 0 1 0 10 8 0 0 0 0 1 0 11 4 0 0 0 0 1 0 12 0 0 0 0 0 1 1 0 39 0 0 0 0 1 1 1 35 0 0 0 0 1 1 2 31 0 0 0 0 1 1 3 27 0 0 0 0 1 1 4 23 0 0 0 0 1 1 5 19 0 0 0 0 1 1 6 15 0 0 0 0 1 1 7 11 0 0 0 0 1 1 8 7 0 0 0 0 1 2 0 30 0 0 0 0 1 2 1 26 0 0 0 0 1 2 2 22 0 0 0 0 1 2 3 18 0 0 0 0 1 2 4 14 0 0 0 0 1 2 5 10 0 0 0 0 1 2 6 6 0 0 0 0 1 3 0 21 0 0 0 0 1 3 1 17 0 0 0 0 1 3 2 13 0 0 0 0 1 3 3 9 0 0 0 0 1 3 4 5 0 0 0 0 2 0 0 32 0 0 0 0 2 0 1 28 0 0 0 0 2 0 2 24 0 0 0 0 2 0 3 20 0 0 0 0 2 0 4 16 0 0 0 0 2 0 5 12 0 0 0 0 2 0 6 8 0 0 0 0 2 0 7 4 0 0 0 0 2 0 8 0 0 0 0 0 2 1 0 23 0 0 0 0 2 1 1 19 0 0 0 0 2 1 2 15 0 0 0 0 2 1 3 11 0 0 0 0 2 1 4 7 0 0 0 0 2 2 0 14 0 0 0 0 2 2 1 10 0 0 0 0 2 2 2 6 0 0 0 0 3 0 0 16 0 0 0 0 3 0 1 12 0 0 0 0 3 0 2 8 0 0 0 0 3 0 3 4 0 0 0 0 3 0 4 0 0 0 0 0 3 1 0 7 0 0 0 0 4 0 0 0 0 0 0 1 0 0 0 39 0 0 0 1 0 0 1 35 0 0 0 1 0 0 2 31 0 0 0 1 0 0 3 27 0 0 0 1 0 0 4 23 0 0 0 1 0 0 5 19 0 0 0 1 0 0 6 15 0 0 0 1 0 0 7 11 0 0 0 1 0 1 0 30 0 0 0 1 0 1 1 26 0 0 0 1 0 1 2 22 0 0 0 1 0 1 3 18 0 0 0 1 0 1 4 14 0 0 0 1 0 1 5 10 0 0 0 1 0 2 0 21 0 0 0 1 0 2 1 17 0 0 0 1 0 2 2 13 0 0 0 1 0 2 3 9 0 0 0 1 0 2 4 5 0 0 0 1 0 3 0 12 0 0 0 1 0 3 1 8 0 0 0 1 0 3 2 4 0 0 1 0 0 0 0 28 0 0 1 0 0 0 1 24 0 0 1 0 0 0 2 20 0 0 1 0 0 0 3 16 0 0 1 0 0 0 4 12 0 0 1 0 0 0 5 8 0 0 1 0 0 0 6 4 0 0 1 0 0 0 7 0 0 1 0 0 0 0 0 15 1 0 0 0 0 0 0 0 A140108(8) = 148 ================================================== Ways to divide a 9 X 9 square into sub-squares: 9 8 7 6 5 4 3 2 1 === === === === === === === === === 0 0 0 0 0 0 0 0 81 0 0 0 0 0 0 0 1 77 0 0 0 0 0 0 0 2 73 0 0 0 0 0 0 0 3 69 0 0 0 0 0 0 0 4 65 0 0 0 0 0 0 0 5 61 0 0 0 0 0 0 0 6 57 0 0 0 0 0 0 0 7 53 0 0 0 0 0 0 0 8 49 0 0 0 0 0 0 0 9 45 0 0 0 0 0 0 0 10 41 0 0 0 0 0 0 0 11 37 0 0 0 0 0 0 0 12 33 0 0 0 0 0 0 0 13 29 0 0 0 0 0 0 0 14 25 0 0 0 0 0 0 0 15 21 0 0 0 0 0 0 0 16 17 0 0 0 0 0 0 1 0 72 0 0 0 0 0 0 1 1 68 0 0 0 0 0 0 1 2 64 0 0 0 0 0 0 1 3 60 0 0 0 0 0 0 1 4 56 0 0 0 0 0 0 1 5 52 0 0 0 0 0 0 1 6 48 0 0 0 0 0 0 1 7 44 0 0 0 0 0 0 1 8 40 0 0 0 0 0 0 1 9 36 0 0 0 0 0 0 1 10 32 0 0 0 0 0 0 1 11 28 0 0 0 0 0 0 1 12 24 0 0 0 0 0 0 1 13 20 0 0 0 0 0 0 1 14 16 0 0 0 0 0 0 1 15 12 0 0 0 0 0 0 2 0 63 0 0 0 0 0 0 2 1 59 0 0 0 0 0 0 2 2 55 0 0 0 0 0 0 2 3 51 0 0 0 0 0 0 2 4 47 0 0 0 0 0 0 2 5 43 0 0 0 0 0 0 2 6 39 0 0 0 0 0 0 2 7 35 0 0 0 0 0 0 2 8 31 0 0 0 0 0 0 2 9 27 0 0 0 0 0 0 2 10 23 0 0 0 0 0 0 2 11 19 0 0 0 0 0 0 2 12 15 0 0 0 0 0 0 2 13 11 0 0 0 0 0 0 2 14 7 0 0 0 0 0 0 3 0 54 0 0 0 0 0 0 3 1 50 0 0 0 0 0 0 3 2 46 0 0 0 0 0 0 3 3 42 0 0 0 0 0 0 3 4 38 0 0 0 0 0 0 3 5 34 0 0 0 0 0 0 3 6 30 0 0 0 0 0 0 3 7 26 0 0 0 0 0 0 3 8 22 0 0 0 0 0 0 3 9 18 0 0 0 0 0 0 3 10 14 0 0 0 0 0 0 3 11 10 0 0 0 0 0 0 3 12 6 0 0 0 0 0 0 3 13 2 0 0 0 0 0 0 4 0 45 0 0 0 0 0 0 4 1 41 0 0 0 0 0 0 4 2 37 0 0 0 0 0 0 4 3 33 0 0 0 0 0 0 4 4 29 0 0 0 0 0 0 4 5 25 0 0 0 0 0 0 4 6 21 0 0 0 0 0 0 4 7 17 0 0 0 0 0 0 4 8 13 0 0 0 0 0 0 4 9 9 0 0 0 0 0 0 4 10 5 0 0 0 0 0 0 5 0 36 0 0 0 0 0 0 5 1 32 0 0 0 0 0 0 5 2 28 0 0 0 0 0 0 5 3 24 0 0 0 0 0 0 5 4 20 0 0 0 0 0 0 5 5 16 0 0 0 0 0 0 5 6 12 0 0 0 0 0 0 5 7 8 0 0 0 0 0 0 5 8 4 0 0 0 0 0 0 5 9 0 0 0 0 0 0 0 6 0 27 0 0 0 0 0 0 6 1 23 0 0 0 0 0 0 6 2 19 0 0 0 0 0 0 6 3 15 0 0 0 0 0 0 6 4 11 0 0 0 0 0 0 6 5 7 0 0 0 0 0 0 7 0 18 0 0 0 0 0 0 7 1 14 0 0 0 0 0 0 7 2 10 0 0 0 0 0 0 7 3 6 0 0 0 0 0 0 8 0 9 0 0 0 0 0 0 8 1 5 0 0 0 0 0 0 9 0 0 0 0 0 0 0 1 0 0 65 0 0 0 0 0 1 0 1 61 0 0 0 0 0 1 0 2 57 0 0 0 0 0 1 0 3 53 0 0 0 0 0 1 0 4 49 0 0 0 0 0 1 0 5 45 0 0 0 0 0 1 0 6 41 0 0 0 0 0 1 0 7 37 0 0 0 0 0 1 0 8 33 0 0 0 0 0 1 0 9 29 0 0 0 0 0 1 0 10 25 0 0 0 0 0 1 0 11 21 0 0 0 0 0 1 0 12 17 0 0 0 0 0 1 1 0 56 0 0 0 0 0 1 1 1 52 0 0 0 0 0 1 1 2 48 0 0 0 0 0 1 1 3 44 0 0 0 0 0 1 1 4 40 0 0 0 0 0 1 1 5 36 0 0 0 0 0 1 1 6 32 0 0 0 0 0 1 1 7 28 0 0 0 0 0 1 1 8 24 0 0 0 0 0 1 1 9 20 0 0 0 0 0 1 1 10 16 0 0 0 0 0 1 1 11 12 0 0 0 0 0 1 2 0 47 0 0 0 0 0 1 2 1 43 0 0 0 0 0 1 2 2 39 0 0 0 0 0 1 2 3 35 0 0 0 0 0 1 2 4 31 0 0 0 0 0 1 2 5 27 0 0 0 0 0 1 2 6 23 0 0 0 0 0 1 2 7 19 0 0 0 0 0 1 2 8 15 0 0 0 0 0 1 2 9 11 0 0 0 0 0 1 2 10 7 0 0 0 0 0 1 3 0 38 0 0 0 0 0 1 3 1 34 0 0 0 0 0 1 3 2 30 0 0 0 0 0 1 3 3 26 0 0 0 0 0 1 3 4 22 0 0 0 0 0 1 3 5 18 0 0 0 0 0 1 3 6 14 0 0 0 0 0 1 3 7 10 0 0 0 0 0 1 3 8 6 0 0 0 0 0 1 3 9 2 0 0 0 0 0 1 4 0 29 0 0 0 0 0 1 4 1 25 0 0 0 0 0 1 4 2 21 0 0 0 0 0 1 4 3 17 0 0 0 0 0 1 4 4 13 0 0 0 0 0 1 4 5 9 0 0 0 0 0 1 4 6 5 0 0 0 0 0 1 5 0 20 0 0 0 0 0 1 5 1 16 0 0 0 0 0 1 5 2 12 0 0 0 0 0 1 5 3 8 0 0 0 0 0 1 5 4 4 0 0 0 0 0 1 5 5 0 0 0 0 0 0 2 0 0 49 0 0 0 0 0 2 0 1 45 0 0 0 0 0 2 0 2 41 0 0 0 0 0 2 0 3 37 0 0 0 0 0 2 0 4 33 0 0 0 0 0 2 0 5 29 0 0 0 0 0 2 0 6 25 0 0 0 0 0 2 0 7 21 0 0 0 0 0 2 0 8 17 0 0 0 0 0 2 1 0 40 0 0 0 0 0 2 1 1 36 0 0 0 0 0 2 1 2 32 0 0 0 0 0 2 1 3 28 0 0 0 0 0 2 1 4 24 0 0 0 0 0 2 1 5 20 0 0 0 0 0 2 1 6 16 0 0 0 0 0 2 1 7 12 0 0 0 0 0 2 2 0 31 0 0 0 0 0 2 2 1 27 0 0 0 0 0 2 2 2 23 0 0 0 0 0 2 2 3 19 0 0 0 0 0 2 2 4 15 0 0 0 0 0 2 2 5 11 0 0 0 0 0 2 2 6 7 0 0 0 0 0 2 3 0 22 0 0 0 0 0 2 3 1 18 0 0 0 0 0 2 3 2 14 0 0 0 0 0 2 3 3 10 0 0 0 0 0 2 3 4 6 0 0 0 0 0 3 0 0 33 0 0 0 0 0 3 0 1 29 0 0 0 0 0 3 0 2 25 0 0 0 0 0 3 0 3 21 0 0 0 0 0 3 0 4 17 0 0 0 0 0 3 1 0 24 0 0 0 0 0 3 1 1 20 0 0 0 0 0 3 1 2 16 0 0 0 0 0 3 1 3 12 0 0 0 0 0 4 0 0 17 0 0 0 0 1 0 0 0 56 0 0 0 0 1 0 0 1 52 0 0 0 0 1 0 0 2 48 0 0 0 0 1 0 0 3 44 0 0 0 0 1 0 0 4 40 0 0 0 0 1 0 0 5 36 0 0 0 0 1 0 0 6 32 0 0 0 0 1 0 0 7 28 0 0 0 0 1 0 0 8 24 0 0 0 0 1 0 0 9 20 0 0 0 0 1 0 0 10 16 0 0 0 0 1 0 0 11 12 0 0 0 0 1 0 0 12 8 0 0 0 0 1 0 1 0 47 0 0 0 0 1 0 1 1 43 0 0 0 0 1 0 1 2 39 0 0 0 0 1 0 1 3 35 0 0 0 0 1 0 1 4 31 0 0 0 0 1 0 1 5 27 0 0 0 0 1 0 1 6 23 0 0 0 0 1 0 1 7 19 0 0 0 0 1 0 1 8 15 0 0 0 0 1 0 1 9 11 0 0 0 0 1 0 1 10 7 0 0 0 0 1 0 1 11 3 0 0 0 0 1 0 2 0 38 0 0 0 0 1 0 2 1 34 0 0 0 0 1 0 2 2 30 0 0 0 0 1 0 2 3 26 0 0 0 0 1 0 2 4 22 0 0 0 0 1 0 2 5 18 0 0 0 0 1 0 2 6 14 0 0 0 0 1 0 2 7 10 0 0 0 0 1 0 2 8 6 0 0 0 0 1 0 3 0 29 0 0 0 0 1 0 3 1 25 0 0 0 0 1 0 3 2 21 0 0 0 0 1 0 3 3 17 0 0 0 0 1 0 3 4 13 0 0 0 0 1 0 3 5 9 0 0 0 0 1 0 3 6 5 0 0 0 0 1 0 4 0 20 0 0 0 0 1 0 4 1 16 0 0 0 0 1 0 4 2 12 0 0 0 0 1 0 5 0 11 0 0 0 0 1 1 0 0 40 0 0 0 0 1 1 0 1 36 0 0 0 0 1 1 0 2 32 0 0 0 0 1 1 0 3 28 0 0 0 0 1 1 0 4 24 0 0 0 0 1 1 0 5 20 0 0 0 0 1 1 0 6 16 0 0 0 0 1 1 0 7 12 0 0 0 0 1 1 0 8 8 0 0 0 0 1 1 1 0 31 0 0 0 0 1 1 1 1 27 0 0 0 0 1 1 1 2 23 0 0 0 0 1 1 1 3 19 0 0 0 0 1 1 1 4 15 0 0 0 0 1 1 1 5 11 0 0 0 0 1 1 1 6 7 0 0 0 0 1 1 1 7 3 0 0 0 0 1 1 2 0 22 0 0 0 0 1 1 2 1 18 0 0 0 0 1 1 2 2 14 0 0 0 0 1 1 2 3 10 0 0 0 0 1 1 2 4 6 0 0 0 0 1 1 3 0 13 0 0 0 0 1 1 3 1 9 0 0 0 0 1 1 3 2 5 0 0 0 0 1 2 0 0 24 0 0 0 0 1 2 0 1 20 0 0 0 0 1 2 0 2 16 0 0 0 0 1 2 0 3 12 0 0 0 0 1 2 0 4 8 0 0 0 0 1 2 1 0 15 0 0 0 0 1 2 1 1 11 0 0 0 0 1 2 1 2 7 0 0 0 0 1 2 1 3 3 0 0 0 0 1 3 0 0 8 0 0 0 1 0 0 0 0 45 0 0 0 1 0 0 0 1 41 0 0 0 1 0 0 0 2 37 0 0 0 1 0 0 0 3 33 0 0 0 1 0 0 0 4 29 0 0 0 1 0 0 0 5 25 0 0 0 1 0 0 0 6 21 0 0 0 1 0 0 0 7 17 0 0 0 1 0 0 1 0 36 0 0 0 1 0 0 1 1 32 0 0 0 1 0 0 1 2 28 0 0 0 1 0 0 1 3 24 0 0 0 1 0 0 1 4 20 0 0 0 1 0 0 1 5 16 0 0 0 1 0 0 1 6 12 0 0 0 1 0 0 2 0 27 0 0 0 1 0 0 2 1 23 0 0 0 1 0 0 2 2 19 0 0 0 1 0 0 2 3 15 0 0 0 1 0 0 2 4 11 0 0 0 1 0 0 2 5 7 0 0 0 1 0 0 3 0 18 0 0 0 1 0 0 3 1 14 0 0 0 1 0 0 3 2 10 0 0 0 1 0 0 3 3 6 0 0 0 1 0 0 4 0 9 0 0 0 1 0 0 4 1 5 0 0 0 1 0 0 5 0 0 0 0 1 0 0 0 0 0 32 0 0 1 0 0 0 0 1 28 0 0 1 0 0 0 0 2 24 0 0 1 0 0 0 0 3 20 0 0 1 0 0 0 0 4 16 0 0 1 0 0 0 0 5 12 0 0 1 0 0 0 0 6 8 0 0 1 0 0 0 0 7 4 0 1 0 0 0 0 0 0 17 1 0 0 0 0 0 0 0 0 A140108(9) = 312 ================================================== Ways to divide a 10 X 10 square into sub-squares: 10 9 8 7 6 5 4 3 2 1 === === === === === === === === === === 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 1 96 0 0 0 0 0 0 0 0 2 92 0 0 0 0 0 0 0 0 3 88 0 0 0 0 0 0 0 0 4 84 0 0 0 0 0 0 0 0 5 80 0 0 0 0 0 0 0 0 6 76 0 0 0 0 0 0 0 0 7 72 0 0 0 0 0 0 0 0 8 68 0 0 0 0 0 0 0 0 9 64 0 0 0 0 0 0 0 0 10 60 0 0 0 0 0 0 0 0 11 56 0 0 0 0 0 0 0 0 12 52 0 0 0 0 0 0 0 0 13 48 0 0 0 0 0 0 0 0 14 44 0 0 0 0 0 0 0 0 15 40 0 0 0 0 0 0 0 0 16 36 0 0 0 0 0 0 0 0 17 32 0 0 0 0 0 0 0 0 18 28 0 0 0 0 0 0 0 0 19 24 0 0 0 0 0 0 0 0 20 20 0 0 0 0 0 0 0 0 21 16 0 0 0 0 0 0 0 0 22 12 0 0 0 0 0 0 0 0 23 8 0 0 0 0 0 0 0 0 24 4 0 0 0 0 0 0 0 0 25 0 0 0 0 0 0 0 0 1 0 91 0 0 0 0 0 0 0 1 1 87 0 0 0 0 0 0 0 1 2 83 0 0 0 0 0 0 0 1 3 79 0 0 0 0 0 0 0 1 4 75 0 0 0 0 0 0 0 1 5 71 0 0 0 0 0 0 0 1 6 67 0 0 0 0 0 0 0 1 7 63 0 0 0 0 0 0 0 1 8 59 0 0 0 0 0 0 0 1 9 55 0 0 0 0 0 0 0 1 10 51 0 0 0 0 0 0 0 1 11 47 0 0 0 0 0 0 0 1 12 43 0 0 0 0 0 0 0 1 13 39 0 0 0 0 0 0 0 1 14 35 0 0 0 0 0 0 0 1 15 31 0 0 0 0 0 0 0 1 16 27 0 0 0 0 0 0 0 1 17 23 0 0 0 0 0 0 0 1 18 19 0 0 0 0 0 0 0 1 19 15 0 0 0 0 0 0 0 1 20 11 0 0 0 0 0 0 0 1 21 7 0 0 0 0 0 0 0 2 0 82 0 0 0 0 0 0 0 2 1 78 0 0 0 0 0 0 0 2 2 74 0 0 0 0 0 0 0 2 3 70 0 0 0 0 0 0 0 2 4 66 0 0 0 0 0 0 0 2 5 62 0 0 0 0 0 0 0 2 6 58 0 0 0 0 0 0 0 2 7 54 0 0 0 0 0 0 0 2 8 50 0 0 0 0 0 0 0 2 9 46 0 0 0 0 0 0 0 2 10 42 0 0 0 0 0 0 0 2 11 38 0 0 0 0 0 0 0 2 12 34 0 0 0 0 0 0 0 2 13 30 0 0 0 0 0 0 0 2 14 26 0 0 0 0 0 0 0 2 15 22 0 0 0 0 0 0 0 2 16 18 0 0 0 0 0 0 0 2 17 14 0 0 0 0 0 0 0 2 18 10 0 0 0 0 0 0 0 2 19 6 0 0 0 0 0 0 0 3 0 73 0 0 0 0 0 0 0 3 1 69 0 0 0 0 0 0 0 3 2 65 0 0 0 0 0 0 0 3 3 61 0 0 0 0 0 0 0 3 4 57 0 0 0 0 0 0 0 3 5 53 0 0 0 0 0 0 0 3 6 49 0 0 0 0 0 0 0 3 7 45 0 0 0 0 0 0 0 3 8 41 0 0 0 0 0 0 0 3 9 37 0 0 0 0 0 0 0 3 10 33 0 0 0 0 0 0 0 3 11 29 0 0 0 0 0 0 0 3 12 25 0 0 0 0 0 0 0 3 13 21 0 0 0 0 0 0 0 3 14 17 0 0 0 0 0 0 0 3 15 13 0 0 0 0 0 0 0 3 16 9 0 0 0 0 0 0 0 3 17 5 0 0 0 0 0 0 0 4 0 64 0 0 0 0 0 0 0 4 1 60 0 0 0 0 0 0 0 4 2 56 0 0 0 0 0 0 0 4 3 52 0 0 0 0 0 0 0 4 4 48 0 0 0 0 0 0 0 4 5 44 0 0 0 0 0 0 0 4 6 40 0 0 0 0 0 0 0 4 7 36 0 0 0 0 0 0 0 4 8 32 0 0 0 0 0 0 0 4 9 28 0 0 0 0 0 0 0 4 10 24 0 0 0 0 0 0 0 4 11 20 0 0 0 0 0 0 0 4 12 16 0 0 0 0 0 0 0 4 13 12 0 0 0 0 0 0 0 4 14 8 0 0 0 0 0 0 0 4 15 4 0 0 0 0 0 0 0 4 16 0 0 0 0 0 0 0 0 5 0 55 0 0 0 0 0 0 0 5 1 51 0 0 0 0 0 0 0 5 2 47 0 0 0 0 0 0 0 5 3 43 0 0 0 0 0 0 0 5 4 39 0 0 0 0 0 0 0 5 5 35 0 0 0 0 0 0 0 5 6 31 0 0 0 0 0 0 0 5 7 27 0 0 0 0 0 0 0 5 8 23 0 0 0 0 0 0 0 5 9 19 0 0 0 0 0 0 0 5 10 15 0 0 0 0 0 0 0 5 11 11 0 0 0 0 0 0 0 5 12 7 0 0 0 0 0 0 0 6 0 46 0 0 0 0 0 0 0 6 1 42 0 0 0 0 0 0 0 6 2 38 0 0 0 0 0 0 0 6 3 34 0 0 0 0 0 0 0 6 4 30 0 0 0 0 0 0 0 6 5 26 0 0 0 0 0 0 0 6 6 22 0 0 0 0 0 0 0 6 7 18 0 0 0 0 0 0 0 6 8 14 0 0 0 0 0 0 0 6 9 10 0 0 0 0 0 0 0 6 10 6 0 0 0 0 0 0 0 6 11 2 0 0 0 0 0 0 0 7 0 37 0 0 0 0 0 0 0 7 1 33 0 0 0 0 0 0 0 7 2 29 0 0 0 0 0 0 0 7 3 25 0 0 0 0 0 0 0 7 4 21 0 0 0 0 0 0 0 7 5 17 0 0 0 0 0 0 0 7 6 13 0 0 0 0 0 0 0 7 7 9 0 0 0 0 0 0 0 7 8 5 0 0 0 0 0 0 0 8 0 28 0 0 0 0 0 0 0 8 1 24 0 0 0 0 0 0 0 8 2 20 0 0 0 0 0 0 0 8 3 16 0 0 0 0 0 0 0 8 4 12 0 0 0 0 0 0 0 9 0 19 0 0 0 0 0 0 1 0 0 84 0 0 0 0 0 0 1 0 1 80 0 0 0 0 0 0 1 0 2 76 0 0 0 0 0 0 1 0 3 72 0 0 0 0 0 0 1 0 4 68 0 0 0 0 0 0 1 0 5 64 0 0 0 0 0 0 1 0 6 60 0 0 0 0 0 0 1 0 7 56 0 0 0 0 0 0 1 0 8 52 0 0 0 0 0 0 1 0 9 48 0 0 0 0 0 0 1 0 10 44 0 0 0 0 0 0 1 0 11 40 0 0 0 0 0 0 1 0 12 36 0 0 0 0 0 0 1 0 13 32 0 0 0 0 0 0 1 0 14 28 0 0 0 0 0 0 1 0 15 24 0 0 0 0 0 0 1 0 16 20 0 0 0 0 0 0 1 0 17 16 0 0 0 0 0 0 1 0 18 12 0 0 0 0 0 0 1 0 19 8 0 0 0 0 0 0 1 0 20 4 0 0 0 0 0 0 1 0 21 0 0 0 0 0 0 0 1 1 0 75 0 0 0 0 0 0 1 1 1 71 0 0 0 0 0 0 1 1 2 67 0 0 0 0 0 0 1 1 3 63 0 0 0 0 0 0 1 1 4 59 0 0 0 0 0 0 1 1 5 55 0 0 0 0 0 0 1 1 6 51 0 0 0 0 0 0 1 1 7 47 0 0 0 0 0 0 1 1 8 43 0 0 0 0 0 0 1 1 9 39 0 0 0 0 0 0 1 1 10 35 0 0 0 0 0 0 1 1 11 31 0 0 0 0 0 0 1 1 12 27 0 0 0 0 0 0 1 1 13 23 0 0 0 0 0 0 1 1 14 19 0 0 0 0 0 0 1 1 15 15 0 0 0 0 0 0 1 1 16 11 0 0 0 0 0 0 1 1 17 7 0 0 0 0 0 0 1 2 0 66 0 0 0 0 0 0 1 2 1 62 0 0 0 0 0 0 1 2 2 58 0 0 0 0 0 0 1 2 3 54 0 0 0 0 0 0 1 2 4 50 0 0 0 0 0 0 1 2 5 46 0 0 0 0 0 0 1 2 6 42 0 0 0 0 0 0 1 2 7 38 0 0 0 0 0 0 1 2 8 34 0 0 0 0 0 0 1 2 9 30 0 0 0 0 0 0 1 2 10 26 0 0 0 0 0 0 1 2 11 22 0 0 0 0 0 0 1 2 12 18 0 0 0 0 0 0 1 2 13 14 0 0 0 0 0 0 1 2 14 10 0 0 0 0 0 0 1 2 15 6 0 0 0 0 0 0 1 3 0 57 0 0 0 0 0 0 1 3 1 53 0 0 0 0 0 0 1 3 2 49 0 0 0 0 0 0 1 3 3 45 0 0 0 0 0 0 1 3 4 41 0 0 0 0 0 0 1 3 5 37 0 0 0 0 0 0 1 3 6 33 0 0 0 0 0 0 1 3 7 29 0 0 0 0 0 0 1 3 8 25 0 0 0 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0 3 1 20 0 0 0 1 0 0 0 3 2 16 0 0 0 1 0 0 0 3 3 12 0 0 0 1 0 0 0 3 4 8 0 0 0 1 0 0 0 4 0 15 0 0 0 1 0 0 0 4 1 11 0 0 0 1 0 0 0 4 2 7 0 0 0 1 0 0 0 4 3 3 0 0 0 1 0 0 0 5 0 6 0 0 1 0 0 0 0 0 0 36 0 0 1 0 0 0 0 0 1 32 0 0 1 0 0 0 0 0 2 28 0 0 1 0 0 0 0 0 3 24 0 0 1 0 0 0 0 0 4 20 0 0 1 0 0 0 0 0 5 16 0 0 1 0 0 0 0 0 6 12 0 0 1 0 0 0 0 0 7 8 0 0 1 0 0 0 0 0 8 4 0 0 1 0 0 0 0 0 9 0 0 1 0 0 0 0 0 0 0 19 1 0 0 0 0 0 0 0 0 0 A140108(10) = 754 ================================================== Ways to divide an 11 X 11 square into sub-squares: 11 10 9 8 7 6 5 4 3 2 1 === === === === === === === === === === === 0 0 0 0 0 0 0 0 0 0 121 0 0 0 0 0 0 0 0 0 1 117 0 0 0 0 0 0 0 0 0 2 113 0 0 0 0 0 0 0 0 0 3 109 0 0 0 0 0 0 0 0 0 4 105 0 0 0 0 0 0 0 0 0 5 101 0 0 0 0 0 0 0 0 0 6 97 0 0 0 0 0 0 0 0 0 7 93 0 0 0 0 0 0 0 0 0 8 89 0 0 0 0 0 0 0 0 0 9 85 0 0 0 0 0 0 0 0 0 10 81 0 0 0 0 0 0 0 0 0 11 77 0 0 0 0 0 0 0 0 0 12 73 0 0 0 0 0 0 0 0 0 13 69 0 0 0 0 0 0 0 0 0 14 65 0 0 0 0 0 0 0 0 0 15 61 0 0 0 0 0 0 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