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

0,2

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).

Formula

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

Example

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

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);

Crossrefs

Cf. A174249, A233427, A247076.

Sequence in context: A020522 A037130 A181298 * A078543 A084128 A044047

Adjacent sequences: A247118 A247119 A247120 * A247122 A247123 A247124

Keyword

nonn

Author

Alois P. Heinz, Nov 19 2014

Status

approved