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%I #12 Feb 06 2017 12:28:12
%S 1,0,2,1,12,10,59,52,276,349,1404,1984,7019,11148,35686,62181,182776,
%T 339350,942507,1841208,4887096,9921685,25442304,53190380,132928715,
%U 284198328,696276202,1514363221,3654567764,8053235650,19212546163,42762014028,101125071372
%N Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, U, X.
%H Alois P. Heinz, <a href="/A278330/b278330.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_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,8,4,21,-8,-4,-6,0,-16,-8).
%F G.f.: -(4*x^6+x^3-1) / (8*x^12 +16*x^11 +6*x^9 +4*x^8 +8*x^7 -21*x^6 -4*x^5 -8*x^4 -2*x^3 -2*x^2+1).
%F a(n) mod 2 = A079978(n).
%e a(2) = 2, a(3) = 1:
%e .___. .___. ._____.
%e | | | | | ._. |
%e | ._| |_. | |_| |_|
%e |_| | | |_| |_ _|
%e | | | | | |_| |
%e |___| |___| |_____| .
%p a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,
%p [-8, -16, 0, -6, -4, -8, 21, 4, 8, 2, 2, 0][j], 0)))^n.
%p <<1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984>>)[1, 1]:
%p seq(a(n), n=0..35);
%Y Cf. A079978, A174249, A233427, A234312, A234931, A247124, A247268, A247443, A249762, A264765, A264812.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Nov 18 2016
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