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%I #16 Oct 18 2018 16:52:46
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,7,1,1,1,2,25,50,25,2,1,1,3,50,
%T 311,311,50,3,1,1,4,155,1954,4101,1954,155,4,1,1,5,508,11914,56864,
%U 56864,11914,508,5,1,1,6,1343,76003,728857,1532496,728857,76003,1343,6,1
%N Number A(n,k) of tilings of a k X n rectangle using pentominoes of any shape and monominoes; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H Alois P. Heinz, <a href="/A278657/b278657.txt">Antidiagonals n = 0..15, flattened</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A(2,3) = A(3,2) = 7:
%e .___. .___. .___. .___. .___. .___. .___.
%e |_|_| | | | | | |_| |_| | | ._| |_. |
%e |_|_| | ._| |_. | | | | | | |_| |_| |
%e |_|_| |_|_| |_|_| |___| |___| |___| |___| .
%e .
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, 2, 3, ...
%e 1, 1, 1, 7, 25, 50, 155, ...
%e 1, 1, 7, 50, 311, 1954, 11914, ...
%e 1, 1, 25, 311, 4101, 56864, 728857, ...
%e 1, 2, 50, 1954, 56864, 1532496, 42238426, ...
%e 1, 3, 155, 11914, 728857, 42238426, 2492016728, ...
%Y Columns (or rows) k=0-7 give: A000012, A003520, A278874, A278875, A278876, A278456, A278877, A278878.
%Y Cf. A174249, A233427.
%K nonn,tabl
%O 0,18
%A _Alois P. Heinz_, Nov 25 2016
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