A295214 - OEIS

%I #21 Nov 22 2017 02:26:10

%S 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,

%T 328,0,16,896,6334,22222,22222,6334,896,16

%N 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.

%C See links.

%H John Mason, <a href="/A295215/a295215.pdf">A theorem about unambiguously decomposable rectangular patterns</a>

%H John Mason, <a href="/A295214/a295214.pdf">Examples of decomposable patterns</a>

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

%e Upper left corner of array:

%e 0,  2,  0,  4,  0, ...

%e 2,  6, 16, 44, ...

%e 0, 16,  0, ...

%e 4, 44, ...

%e 0, ...

%e ...

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

%K nonn,tabl,more

%O 1,2

%A _John Mason_, Nov 17 2017