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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 July 23 08:59 EDT 2017. Contains 289686 sequences.