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.
Original entry on oeis.org
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
Offset: 0
A(2,3) = A(3,2) = 7:
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|_|_| | | | | | |_| |_| | | ._| |_. |
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.
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, ...
A278964
Number of tilings of a 6 X n rectangle using pentominoes of shapes L, U, X and monominoes.
Original entry on oeis.org
1, 1, 31, 432, 9851, 150749, 2392788, 38885816, 646657365, 10599739324, 173226495187, 2835753730682, 46501906844608, 762113847626540, 12484929995911672, 204541850515528677, 3351522453919340317, 54915791725126323755, 899777273419073185968
Offset: 0
a(2) = 31:
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.___. .___. .___. .___. .___. .___. .___. .___. .___. .___. .___.
| ._| |_. | | |_| |_|_| |_|_| |_. | |_. | |_|_| |_. | |_|_| |_|_|
| |_| |_| | | |_| | |_| |_|_| | | | |_| | |_. | |_| | |_. | |_|_|
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|___| |___| |_|_| |_|_| |___| |_|_| |___| |___| |_|_| |_|_| |_|_|
.___. .___. .___. .___. .___. .___. .___. .___. .___.
| ._| |_|_| |_|_| | ._| | ._| |_|_| |_|_| |_|_| |_| |
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|_|_| | |_| | |_| |_| | |_| | | | | |_| | |_| | |___|
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A286347
Number of tilings of a 6 X n rectangle using pentominoes of shapes X, Y, T and monominoes.
Original entry on oeis.org
1, 1, 15, 188, 3763, 54368, 790504, 11771179, 176285795, 2627027061, 39172906410, 584774465361, 8725442013820, 130117410190768, 1940656499251689, 28950613608637003, 431889355175650435, 6442566792491842258, 96102610815876310611, 1433558139553752297236
Offset: 0
A286391
Number of tilings of a 6 X n rectangle using pentominoes of shapes X, Y, Z, T and monominoes.
Original entry on oeis.org
1, 1, 15, 344, 6835, 119392, 2136080, 38329669, 688355077, 12374676591, 222673114420, 4005005917279, 72004800735036, 1294444641691072, 23273376392535695, 418470613768822683, 7524342117053834729, 135288703461639048592, 2432489164334993344213
Offset: 0
a(2) = 15:
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