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 A227690 Number A(n,k) of tilings of a k X n rectangle using integer sided square tiles reduced for symmetry; square array A(n,k), n>=0, k>=0, read by antidiagonals. 5
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 3, 4, 1, 1, 1, 1, 5, 6, 6, 5, 1, 1, 1, 1, 9, 10, 13, 10, 9, 1, 1, 1, 1, 12, 21, 39, 39, 21, 12, 1, 1, 1, 1, 21, 39, 115, 77, 115, 39, 21, 1, 1, 1, 1, 30, 82, 295, 521, 521, 295, 82, 30, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Square array A(n,k) begins: 1, 1,  1,  1,   1,    1,     1,      1,       1, ... 1, 1,  1,  1,   1,    1,     1,      1,       1, ... 1, 1,  2,  2,   4,    5,     9,     12,      21, ... 1, 1,  2,  3,   6,   10,    21,     39,      82, ... 1, 1,  4,  6,  13,   39,   115,    295,     861, ... 1, 1,  5, 10,  39,   77,   521,   1985,    8038, ... 1, 1,  9, 21, 115,  521,  1494,  15129,   83609, ... 1, 1, 12, 39, 295, 1985, 15129,  56978,  861159, ... 1, 1, 21, 82, 861, 8038, 83609, 861159, 4495023, ... LINKS Christopher Hunt Gribble, Antidiagonals n = 0..15, flattened Christopher Hunt Gribble, C++ program EXAMPLE A(4,3) = 6 because there are 6 ways to tile a 3 X 4 rectangle by sub-squares, reduced for symmetry i.e. where rotations and reflections are not counted as distinct: ._____ _.    ._______.    ._______. |     |_|    |   |   |    |   |_|_| |     |_|    |___|_ _|    |___|   | |_____|_|    |_|_|_|_|    |_|_|___| ._______.    ._______.    ._______. |   |_|_|    |_|   |_|    |_|_|_|_| |___|_|_|    |_|___|_|    |_|_|_|_| |_|_|_|_|    |_|_|_|_|    |_|_|_|_| CROSSREFS Column (or row) k=2 gives: A001224. Diagonal gives: A224239. Cf. A219924, A224697. Sequence in context: A067059 A049704 A047996 * A063686 A008327 A133687 Adjacent sequences:  A227687 A227688 A227689 * A227691 A227692 A227693 KEYWORD nonn,tabl AUTHOR Christopher Hunt Gribble, Jul 19 2013 STATUS approved

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Last modified December 11 13:08 EST 2018. Contains 318049 sequences. (Running on oeis4.)