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A247121 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes P, U. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)