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 A182106 Number of tilings of an n X n square with rectangles with integer sides and area n. 1
 1, 1, 2, 2, 9, 2, 46, 2, 250, 37, 254, 2, 31052, 2, 1480, 896, 306174, 2, 2097506, 2, 6025516, 6638, 59930, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Dividing a square into equal-sized rectangles at math.stackexchange PROG (Java) public class Question130758 {     final static int maxn = 23;     static int n;     static int [] divisors = new int [maxn];     static int ndivisors;     static boolean [] [] grid;     static int count;     public static void main (String [] args) {         for (n = 0; n <= maxn; n++) {             ndivisors = 0;             for (int divisor = 1; divisor <= n; divisor++)                 if (n % divisor == 0)                     divisors [ndivisors++] = divisor;             grid = new boolean [n] [n];             count = 0;             recurse (0, 0, 0);             System.out.print (count + ", ");         }         System.out.println ();     }     static void recurse (int x, int y, int depth) {         if (depth == n) {             count++;             return;         }         while (grid [x] [y])             if (++x == n) {                 x = 0;                 y++;             }         outer:         for (int k = 0; k < ndivisors; k++) {             int w = divisors [k];             int h = n / w;             if (x + w > n || y + h > n)                 continue;             for (int i = 0; i < w; i++)                 for (int j = 0; j < h; j++)                     if (grid [x + i] [y + j])                         continue outer;             for (int i = 0; i < w; i++)                 for (int j = 0; j < h; j++)                     grid [x + i] [y + j] = true;             recurse (x, y, depth + 1);             for (int i = 0; i < w; i++)                 for (int j = 0; j < h; j++)                     grid [x + i] [y + j] = false;         }     } } CROSSREFS Diagonal of A220122. - Alois P. Heinz, Dec 07 2012 Sequence in context: A108462 A327859 A343824 * A308037 A011403 A113554 Adjacent sequences:  A182103 A182104 A182105 * A182107 A182108 A182109 KEYWORD nonn AUTHOR Felix A. Pahl, Apr 12 2012 STATUS approved

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Last modified December 8 03:17 EST 2021. Contains 349590 sequences. (Running on oeis4.)