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%I A278330 #12 Feb 06 2017 12:28:12
%S A278330 1,0,2,1,12,10,59,52,276,349,1404,1984,7019,11148,35686,62181,182776,
%T A278330 339350,942507,1841208,4887096,9921685,25442304,53190380,132928715,
%U A278330 284198328,696276202,1514363221,3654567764,8053235650,19212546163,42762014028,101125071372
%N A278330 Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, U, X.
%H A278330 Alois P. Heinz, <a href="/A278330/b278330.txt">Table of n, a(n) for n = 0..1000</a>
%H A278330 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A278330 <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 A278330 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 A278330 a(n) mod 2 = A079978(n).
%e A278330 a(2) = 2,          a(3) = 1:
%e A278330 .___.   .___.      ._____.
%e A278330 |   |   |   |      | ._. |
%e A278330 | ._|   |_. |      |_| |_|
%e A278330 |_| |   | |_|      |_   _|
%e A278330 |   |   |   |      | |_| |
%e A278330 |___|   |___|      |_____| .
%p A278330 a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,
%p A278330     [-8, -16, 0, -6, -4, -8, 21, 4, 8, 2, 2, 0][j], 0)))^n.
%p A278330     <<1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984>>)[1, 1]:
%p A278330 seq(a(n), n=0..35);
%Y A278330 Cf. A079978, A174249, A233427, A234312, A234931, A247124, A247268, A247443, A249762, A264765, A264812.
%K A278330 nonn,easy
%O A278330 0,3
%A A278330 _Alois P. Heinz_, Nov 18 2016

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