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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
OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 19 2014
STATUS
approved