A174249
Number of tilings of a 5 X n rectangle with n pentominoes of any shape.
Original entry on oeis.org
1, 1, 5, 56, 501, 4006, 27950, 214689, 1696781, 13205354, 101698212, 782267786, 6048166230, 46799177380, 361683136647, 2793722300087, 21583392631817, 166790059833039, 1288885349447958, 9959188643348952, 76953117224941654, 594617039453764617, 4594660583890506956
Offset: 0
Bob Harris (me13013(AT)gmail.com), Mar 13 2010
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Jessica Gonzalez, Illustration for a(2) = 5
- R. S. Harris, Counting Nonomino Tilings and Other Things of that Ilk, G4G9 Gift Exchange book, 2010.
- R. S. Harris, Counting Polyomino Tilings
- Vaclav Kotesovec, G.f. and the recurrence (of order 324)
- Wikipedia, Pentomino
- Index entries for linear recurrences with constant coefficients, order 324.
Row sums of
A247702,
A247703,
A247704,
A247705,
A247706,
A247707,
A247708,
A247709,
A247710,
A247711,
A247712,
A247713.
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:
.___. .___. .___. .___. .___. .___. .___.
|_|_| | | | | | |_| |_| | | ._| |_. |
|_|_| | ._| |_. | | | | | | |_| |_| |
|_|_| |_|_| |_|_| |___| |___| |___| |___| .
.
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:
.___. .___. .___. .___. .___. .___. .___. .___. .___. .___. .___.
|_|_| | ._| | ._| |_|_| |_|_| |_|_| |_. | |_. | |_|_| |_|_| |_|_|
|_|_| | |_| | |_| | ._| |_|_| |_|_| |_| | |_| | |_. | |_|_| |_|_|
|_|_| |___| |___| | |_| | ._| |_|_| |___| |___| |_| | |_. | |_|_|
|_|_| | ._| |_|_| |___| | |_| | ._| |_. | |_|_| |___| |_| | |_. |
|_|_| | |_| |_|_| |_|_| |___| | |_| |_| | |_|_| |_|_| |___| |_| |
|_|_| |___| |_|_| |_|_| |_|_| |___| |___| |_|_| |_|_| |_|_| |___|
.___. .___. .___. .___. .___. .___. .___. .___. .___. .___. .___.
| ._| |_. | | |_| |_|_| |_|_| |_. | |_. | |_|_| |_. | |_|_| |_|_|
| |_| |_| | | |_| | |_| |_|_| | | | |_| | |_. | |_| | |_. | |_|_|
|___| |___| | |_| | |_| | |_| | | | | | | | | | |_| | |_| | |_. |
|_. | | ._| |___| | |_| | |_| | |_| | |_| | | | |_|_| |_| | |_| |
|_| | | |_| |_|_| |___| | |_| |___| | |_| | |_| |_|_| |_|_| |_| |
|___| |___| |_|_| |_|_| |___| |_|_| |___| |___| |_|_| |_|_| |_|_|
.___. .___. .___. .___. .___. .___. .___. .___. .___.
| ._| |_|_| |_|_| | ._| | ._| |_|_| |_|_| |_|_| |_| |
| |_| | ._| |_|_| | | | | |_| | ._| |_|_| |_| | |_| |
| |_| | |_| | ._| | | | | | | | | | |_| | |_| | |_| |
|_|_| | |_| | |_| |_| | |_| | | | | |_| | |_| | |___|
|_|_| |_|_| | |_| |___| |_| | |_| | |_| | |___| |_|_|
|_|_| |_|_| |_|_| |_|_| |___| |___| |___| |_|_| |_|_| .
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:
.___. .___. .___. .___. .___. .___. .___. .___. .___.
|_|_| | |_| |_| | | |_| |_|_| |_|_| |_|_| |_|_| | |_|
|_|_| | ._| |_. | | ._| | |_| |_|_| |_|_| | |_| | |_|
|_|_| | | | | | | | |_| | ._| | |_| | |_| | |_| | ._|
|_|_| |_| | | |_| |_|_| | |_| | ._| | |_| | ._| |_|_|
|_|_| |_. | | ._| |_|_| |_|_| | |_| | ._| |_|_| |_|_|
|_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |_|_|
.___. .___. .___. .___. .___. .___.
|_| | |_|_| |_|_| |_|_| |_|_| |_| |
|_. | |_| | |_|_| |_|_| |_| | |_| |
|_| | |_. | |_| | |_| | |_| | |_. |
|_|_| |_| | |_. | |_| | |_. | |_|_|
|_|_| |_|_| |_| | |_. | |_|_| |_|_|
|_|_| |_|_| |_|_| |_|_| |_|_| |_|_| .
Showing 1-5 of 5 results.
