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

Author

Alois P. Heinz, Sep 22 2014

Keywords

• nonn

Examples

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

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

Crossrefs

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

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