A295214 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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