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A278657 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. 11
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, 311, 311, 50, 3, 1, 1, 4, 155, 1954, 4101, 1954, 155, 4, 1, 1, 5, 508, 11914, 56864, 56864, 11914, 508, 5, 1, 1, 6, 1343, 76003, 728857, 1532496, 728857, 76003, 1343, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,18

LINKS

Alois P. Heinz, Antidiagonals n = 0..15, flattened

Wikipedia, Pentomino

EXAMPLE

A(2,3) = A(3,2) = 7:

  .___.  .___.  .___.  .___.  .___.  .___.  .___.

  |_|_|  |   |  |   |  | |_|  |_| |  | ._|  |_. |

  |_|_|  | ._|  |_. |  |   |  |   |  | |_|  |_| |

  |_|_|  |_|_|  |_|_|  |___|  |___|  |___|  |___| .

.

Square array A(n,k) begins:

  1, 1,   1,     1,      1,        1,          1, ...

  1, 1,   1,     1,      1,        2,          3, ...

  1, 1,   1,     7,     25,       50,        155, ...

  1, 1,   7,    50,    311,     1954,      11914, ...

  1, 1,  25,   311,   4101,    56864,     728857, ...

  1, 2,  50,  1954,  56864,  1532496,   42238426, ...

  1, 3, 155, 11914, 728857, 42238426, 2492016728, ...

CROSSREFS

Columns (or rows) k=0-7 give: A000012, A003520, A278874, A278875, A278876, A278456, A278877, A278878.

Cf. A174249, A233427.

Sequence in context: A258149 A278717 A241009 * A242914 A046542 A172351

Adjacent sequences:  A278654 A278655 A278656 * A278658 A278659 A278660

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Nov 25 2016

STATUS

approved

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Last modified July 30 03:31 EDT 2021. Contains 346347 sequences. (Running on oeis4.)