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%I #13 Feb 07 2017 10:38:17
%S 1,0,0,18,24,238,842,4360,25900,112178,613140,2941170,14789274,
%T 74895336,369603312,1866863986,9294391952,46543456838,233028690018,
%U 1164275409976,5830080180396,29149585256266,145845002931724,729627382873090,3649578988919810
%N Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes N, Y.
%H Alois P. Heinz, <a href="/A248102/b248102.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F G.f.: (8*x^15 -52*x^14 -64*x^13 +1087*x^12 -2822*x^11 +2369*x^10 +810*x^9 -2047*x^8 +300*x^7 +122*x^6 +208*x^5 +x^4 +6*x^3 +9*x^2 +2*x -1) / (24*x^15 +4*x^14 -680*x^13 +2673*x^12 -4212*x^11 +2139*x^10 +1574*x^9 -2141*x^8 +456*x^7 -160*x^6 +236*x^5 -11*x^4 +24*x^3 +9*x^2 +2*x -1).
%e a(3) = 18:
%e ._______._._. .___._______. .___._______.
%e |_. .___| | | |_. |___. ._| |_. |___. ._|
%e | |_| | ._| | | |_____|_| | | |_____|_| |
%e | ._| | |_. | | |___. ._| | | |___. |_. |
%e | | ._|_| |_| | ._| |_|_. | | ._| |___| |
%e |_|_|_______| (*2) |_|_______|_| (*8) |_|_______|_| (*8) .
%Y Cf. A174249, A233427, A234312, A234931, A247680, A247443.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Oct 01 2014