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%I #36 Jul 26 2023 19:41:59
%S 1,1,1,1,0,1,1,0,0,1,1,1,0,1,1,1,0,3,3,0,1,1,0,0,10,0,0,1,1,1,0,23,23,
%T 0,1,1,1,0,11,62,0,62,11,0,1,1,0,0,170,0,0,170,0,0,1,1,1,0,441,939,0,
%U 939,441,0,1,1,1,0,41,1173,0,8342,8342,0,1173,41,0,1
%N Number A(n,k) of tilings of a k X n rectangle using trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%C Every row and column satisfies a linear recurrence. - _Peter Kagey_, Jul 17 2019
%H Alois P. Heinz, <a href="/A233320/b233320.txt">Antidiagonals n = 0..28, flattened</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tromino">Tromino</a>
%F A(n,k) = 0 <=> n*k mod 3 > 0.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 0, 0, 1, 0, 0, 1, ...
%e 1, 0, 0, 3, 0, 0, 11, ...
%e 1, 1, 3, 10, 23, 62, 170, ...
%e 1, 0, 0, 23, 0, 0, 939, ...
%e 1, 0, 0, 62, 0, 0, 8342, ...
%e 1, 1, 11, 170, 939, 8342, 80092, ...
%e 1, 0, 0, 441, 0, 0, 614581, ...
%e 1, 0, 0, 1173, 0, 0, 5271923, ...
%Y Columns (or rows) include: A000012, A001835, A134438, A233339, A233340, A233290, A233343, A269958, A215826, A269959, A269664.
%Y Cf. A099390, A230031, A233427, A270061, A364457.
%K nonn,tabl
%O 0,18
%A _Alois P. Heinz_, Dec 07 2013
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