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A247125 Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, U, X.

%I A247125 #19 Feb 06 2017 18:40:08
%S A247125 1,0,2,1,16,10,59,60,330,397,1520,2218,7875,12820,39250,70045,202168,
%T A247125 384866,1038051,2073580,5385754,11156701,28015232,59580154,146333795,
%U A247125 317517636,766142242,1686735709,4019319048,8946988370,21116854115,47386013020,111065223914
%N A247125 Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, U, X.
%H A247125 Alois P. Heinz, <a href="/A247125/b247125.txt">Table of n, a(n) for n = 0..1000</a>
%H A247125 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A247125 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,12,6,2).
%F A247125 G.f.: -1/(2*x^6+6*x^5+12*x^4+x^3+2*x^2-1).
%e A247125 a(4) = 16:
%e A247125 ._______.     ._______.     ._______.
%e A247125 | ._____|     | ._____|     | ._| ._|
%e A247125 |_| |_. |     |_| |_. |     | | | | |
%e A247125 |_. ._| |     |_. ._| |     | | | | |
%e A247125 | |_|___|     | |_| | |     |_| |_| |
%e A247125 |_______| (2) |_____|_| (4) |___|___| (4)
%e A247125 ._______.     ._______.
%e A247125 | ._____|     | ._____|
%e A247125 |_| ._. |     |_|_. | |
%e A247125 | |_| |_|     | ._| | |
%e A247125 |_____| |     | |___| |
%e A247125 |_______| (2) |___|___| (4) .
%p A247125 a:= n-> (<<0|1|0|0|0|0>, <0|0|1|0|0|0>, <0|0|0|1|0|0>,
%p A247125           <0|0|0|0|1|0>, <0|0|0|0|0|1>, <2|6|12|1|2|0>>^n)[6,6]:
%p A247125 seq(a(n), n=0..40);
%Y A247125 Cf. A174249, A233427, A234312, A247124, A247268.
%K A247125 nonn
%O A247125 0,3
%A A247125 _Alois P. Heinz_, Nov 19 2014