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 A233427 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. 76
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,31 LINKS Alois P. Heinz, Antidiagonals n = 0..17, flattened R. S. Harris, Counting Polyomino Tilings Wikipedia, Pentomino FORMULA A(n,k) = 0 <=> n*k mod 5 > 0. EXAMPLE A(5,2) = A(2,5) = 5:   ._________. ._________. ._________. ._________. ._________.   |_________| | ._____| | | |_____. | |   ._|   | |   |_.   |   |_________| |_|_______| |_______|_| |___|_____| |_____|___|. Square array A(n,k) begins:   1, 1,  1,    1,      1,         1,          1, ...   1, 0,  0,    0,      0,         1,          0, ...   1, 0,  0,    0,      0,         5,          0, ...   1, 0,  0,    0,      0,        56,          0, ...   1, 0,  0,    0,      0,       501,          0, ...   1, 1,  5,   56,    501,      4006,      27950, ...   1, 0,  0,    0,      0,     27950,          0, ...   1, 0,  0,    0,      0,    214689,          0, ...   1, 0,  0,    0,      0,   1696781,          0, ...   1, 0,  0,    0,      0,  13205354,          0, ...   1, 1, 45, 7670, 890989, 101698212, 7845888732, ...   ... CROSSREFS Columns (or rows) include: A000012, A054318, A233428, A233429, A174249, A233430. Cf. A099390, A233320, A230031, A246902, A247117, A278657. Row sums of A247702, A247703, A247704, A247705, A247706, A247707, A247708, A247709, A247710, A247711, A247712, A247713 give A(n,5). Sequence in context: A105077 A073231 A099223 * A237660 A261852 A254293 Adjacent sequences:  A233424 A233425 A233426 * A233428 A233429 A233430 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Dec 09 2013 STATUS approved

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Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)