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%I #13 Oct 18 2018 16:25:08
%S 1,1,1,1,1,1,1,1,1,1,1,2,5,2,1,1,3,14,14,3,1,1,4,45,93,45,4,1,1,6,140,
%T 590,590,140,6,1,1,9,438,3710,7517,3710,438,9,1,1,13,1371,23509,96176,
%U 96176,23509,1371,13,1,1,19,4287,148796,1238818,2501946,1238818,148796,4287,19,1
%N Number A(n,k) of tilings of a k X n rectangle using monominoes and trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H Alois P. Heinz, <a href="/A270061/b270061.txt">Antidiagonals n = 0..25, flattened</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tromino">Tromino</a>
%e A(2,3) = A(3,2) = 14:
%e ._____. ._____. ._____. ._____. ._____. ._____. ._____.
%e |_____| |_|_|_| |_____| |_| |_| | |_|_| | ._|_| |_. |_|
%e |_____| |_____| |_|_|_| |___|_| |___|_| |_|_|_| |_|_|_|
%e .
%e ._____. ._____. ._____. ._____. ._____. ._____. ._____.
%e |_|_|_| | ._| | | |_. | |_|_| | |_| |_| |_| ._| |_|_. |
%e |_|_|_| |_|___| |___|_| |_|___| |_|___| |_|_|_| |_|_|_| .
%e .
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 2, 3, 4, 6, ...
%e 1, 1, 5, 14, 45, 140, 438, ...
%e 1, 2, 14, 93, 590, 3710, 23509, ...
%e 1, 3, 45, 590, 7517, 96176, 1238818, ...
%e 1, 4, 140, 3710, 96176, 2501946, 65410388, ...
%e 1, 6, 438, 23509, 1238818, 65410388, 3473827027, ...
%Y Columns (or rows) k=0-10 give: A000012, A000930, A270062, A270063, A270064, A270065, A270066, A270067, A270068, A270069, A270070.
%Y Main diagonal gives A270071.
%Y Cf. A233320.
%K nonn,tabl
%O 0,12
%A _Alois P. Heinz_, Mar 09 2016
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