A247121 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes P, U.

1, 2, 12, 56, 248, 1184, 5472, 25376, 118208, 548864, 2550912, 11856896, 55098368, 256070144, 1190065152, 5530658816, 25703241728, 119453057024, 555145224192, 2579979739136, 11990182412288, 55723107221504, 258967268524032, 1203523043065856, 5593246378754048

Offset: 0

Author

Alois P. Heinz, Nov 19 2014

Keywords

• nonn

Examples

			a(2) = 12:
._______.      ._______.      ._______.      ._______.
|   |   |      |   ._| |      | ._|   |      | ._|   |
| ._| ._|      |___|   |      | |_____|      | |_____|
|_| |_| |      |   |___|      |___|   |      |___|_. |
|   |   |      | ._|   |      |   |_. |      |   ._| |
|___|___| (*4) |_|_____| (*2) |_____|_| (*4) |___|___| (*2) .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Pentomino
• Index entries for linear recurrences with constant coefficients, signature (2,8,20).

Crossrefs

Cf. A174249, A233427, A247076.

Programs

Maple

a:= n-> ceil((<<0|1|0>, <0|0|1>, <20|8|2>>^(n-1). <<2, 12, 56>>)[1, 1]):
seq(a(n), n=0..30);

Formula

G.f.: (4*x^3-1)/(20*x^3+8*x^2+2*x-1).