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%I #16 Feb 06 2017 18:34:43
%S 1,2,12,56,248,1184,5472,25376,118208,548864,2550912,11856896,
%T 55098368,256070144,1190065152,5530658816,25703241728,119453057024,
%U 555145224192,2579979739136,11990182412288,55723107221504,258967268524032,1203523043065856,5593246378754048
%N Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes P, U.
%H Alois P. Heinz, <a href="/A247121/b247121.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,20).
%F G.f.: (4*x^3-1)/(20*x^3+8*x^2+2*x-1).
%e a(2) = 12:
%e ._______. ._______. ._______. ._______.
%e | | | | ._| | | ._| | | ._| |
%e | ._| ._| |___| | | |_____| | |_____|
%e |_| |_| | | |___| |___| | |___|_. |
%e | | | | ._| | | |_. | | ._| |
%e |___|___| (*4) |_|_____| (*2) |_____|_| (*4) |___|___| (*2) .
%p a:= n-> ceil((<<0|1|0>, <0|0|1>, <20|8|2>>^(n-1). <<2, 12, 56>>)[1, 1]):
%p seq(a(n), n=0..30);
%Y Cf. A174249, A233427, A247076.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Nov 19 2014
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