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%I #19 Feb 06 2017 18:40:08
%S 1,0,2,1,16,10,59,60,330,397,1520,2218,7875,12820,39250,70045,202168,
%T 384866,1038051,2073580,5385754,11156701,28015232,59580154,146333795,
%U 317517636,766142242,1686735709,4019319048,8946988370,21116854115,47386013020,111065223914
%N Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, U, X.
%H Alois P. Heinz, <a href="/A247125/b247125.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,12,6,2).
%F G.f.: -1/(2*x^6+6*x^5+12*x^4+x^3+2*x^2-1).
%e a(4) = 16:
%e ._______. ._______. ._______.
%e | ._____| | ._____| | ._| ._|
%e |_| |_. | |_| |_. | | | | | |
%e |_. ._| | |_. ._| | | | | | |
%e | |_|___| | |_| | | |_| |_| |
%e |_______| (2) |_____|_| (4) |___|___| (4)
%e ._______. ._______.
%e | ._____| | ._____|
%e |_| ._. | |_|_. | |
%e | |_| |_| | ._| | |
%e |_____| | | |___| |
%e |_______| (2) |___|___| (4) .
%p a:= n-> (<<0|1|0|0|0|0>, <0|0|1|0|0|0>, <0|0|0|1|0|0>,
%p <0|0|0|0|1|0>, <0|0|0|0|0|1>, <2|6|12|1|2|0>>^n)[6,6]:
%p seq(a(n), n=0..40);
%Y Cf. A174249, A233427, A234312, A247124, A247268.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Nov 19 2014
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