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%I #36 Nov 06 2018 21:29:44
%S 1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,5,0,0,5,
%T 0,1,1,0,0,56,0,56,0,0,1,1,0,0,0,501,501,0,0,0,1,1,0,0,0,0,4006,0,0,0,
%U 0,1,1,1,0,0,0,27950,27950,0,0,0,1,1,1,0,45,0,0,214689,0,214689,0,0,45,0,1
%N Number A(n,k) of tilings of a k X n rectangle using pentominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H Alois P. Heinz, <a href="/A233427/b233427.txt">Antidiagonals n = 0..17, flattened</a>
%H R. S. Harris, <a href="http://www.bumblebeagle.org/polyominoes/tilingcounting">Counting Polyomino Tilings</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F A(n,k) = 0 <=> n*k mod 5 > 0.
%e A(5,2) = A(2,5) = 5:
%e ._________. ._________. ._________. ._________. ._________.
%e |_________| | ._____| | | |_____. | | ._| | | |_. |
%e |_________| |_|_______| |_______|_| |___|_____| |_____|___|.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 0, 0, 0, 0, 1, 0, ...
%e 1, 0, 0, 0, 0, 5, 0, ...
%e 1, 0, 0, 0, 0, 56, 0, ...
%e 1, 0, 0, 0, 0, 501, 0, ...
%e 1, 1, 5, 56, 501, 4006, 27950, ...
%e 1, 0, 0, 0, 0, 27950, 0, ...
%e 1, 0, 0, 0, 0, 214689, 0, ...
%e 1, 0, 0, 0, 0, 1696781, 0, ...
%e 1, 0, 0, 0, 0, 13205354, 0, ...
%e 1, 1, 45, 7670, 890989, 101698212, 7845888732, ...
%e ...
%Y Columns (or rows) include: A000012, A054318, A233428, A233429, A174249, A233430.
%Y Cf. A099390, A233320, A230031, A246902, A247117, A278657.
%Y Row sums of A247702, A247703, A247704, A247705, A247706, A247707, A247708, A247709, A247710, A247711, A247712, A247713 give A(n,5).
%K nonn,tabl
%O 0,31
%A _Alois P. Heinz_, Dec 09 2013
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