A247680 Number of tilings of a 5 X n rectangle using n pentominoes of shapes W, I, L, F.

1, 1, 3, 5, 21, 82, 249, 688, 1879, 5690, 17932, 55271, 164427, 485348, 1451110, 4395114, 13313135, 40073992, 120200822, 360897368, 1086543152, 3274191643, 9858847241, 29657925485, 89206237151, 268435863317, 808022052324, 2432169981689, 7319562671432

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, G.f. and the recurrence (of order 324)

Wikipedia, Pentomino

Formula

a(n) ~ c * d^n, where d = 3.009533036298033336764263169394953980849599088993157702490314631810945318907..., c = 0.29272000293879867768013500033525343337565088925220444775140709413075274... (1/d is the root of the denominator, see g.f.). - Vaclav Kotesovec, May 19 2015

Example

a(3) = 5:
._____.  ._____.  ._____.  ._____.  ._____.
| | | |  | |_. |  | ._| |  | | ._|  |_. | |
| | | |  | | | |  | | | |  | | | |  | | | |
| | | |  | | | |  | | | |  | | | |  | | | |
| | | |  | | |_|  |_| | |  | |_| |  | |_| |
|_|_|_|  |_|___|  |___|_|  |_|___|  |___|_|.
a(4) = 21:
._______.  ._______.
|_. |_. |  | ._| ._|
| |_. | |  | |_. | |
|_. |_| |  | | |_| |
| |___|_|  |_| ._| |
|_______|  |___|___| ... .

Crossrefs

Cf. A174249, A233427, A234312, A234931, A247443, A249762, A257866.

Sequence in context: A196418 A189560 A216385 * A179265 A084253 A153889

Adjacent sequences: A247677 A247678 A247679 * A247681 A247682 A247683

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2014

Status

approved