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.

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

Offset: 0

Author

Christopher Hunt Gribble, Jul 19 2013

Keywords

• nonn
• tabl

Examples

			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, ...
...
A(4,3) = 6 because there are 6 ways to tile a 3 X 4 rectangle by subsquares, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct:
   ._____ _.    ._______.    ._______.
   |     |_|    |   |   |    |   |_|_|
   |     |_|    |___|_ _|    |___|   |
   |_____|_|    |_|_|_|_|    |_|_|___|
   ._______.    ._______.    ._______.
   |   |_|_|    |_|   |_|    |_|_|_|_|
   |___|_|_|    |_|___|_|    |_|_|_|_|
   |_|_|_|_|    |_|_|_|_|    |_|_|_|_|
		

Links

• Christopher Hunt Gribble, Antidiagonals n = 0..15, flattened
• Christopher Hunt Gribble, C++ program

Crossrefs

Main diagonal: A224239.

Columns 1-10: A000012, A001224, A359019, A359020, A359021, A359022, A359023, A359024, A359025, A359026.

Cf. A219924, A224697.