A295214 Array T(m,n) read by antidiagonals: number of m X n rectangular patterns of precisely half black squares and half white squares that are tilable with black and white colored dominoes, for m >= 1, n >= 1.

0, 2, 2, 0, 6, 0, 4, 16, 16, 4, 0, 44, 0, 44, 0, 8, 120, 318, 318, 120, 8, 0, 328, 0, 2798, 0, 328, 0, 16, 896, 6334, 22222, 22222, 6334, 896, 16

Offset

1,2

Comments

See links.

Links

Table of n, a(n) for n=1..36.

John Mason, A theorem about unambiguously decomposable rectangular patterns

John Mason, Examples of decomposable patterns

Formula

a(n) = A295215(n) + A295216(n).

Example

Upper left corner of array:
0,  2,  0,  4,  0, ...
2,  6, 16, 44, ...
0, 16,  0, ...
4, 44, ...
0, ...
...

Crossrefs

Cf. A295215 (unambiguously tilable patterns), A295216 (ambiguously tilable patterns), A004003 (domino tiling of a square), A099390 (domino tiling of a rectangle).

Sequence in context: A254749 A129936 A253180 * A221408 A221396 A221337

Adjacent sequences: A295211 A295212 A295213 * A295215 A295216 A295217

Keyword

nonn,tabl,more

Author

John Mason, Nov 17 2017

Status

approved