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A247126 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, U, X, N.

%I A247126 #14 Feb 06 2017 18:53:55
%S A247126 1,0,0,1,2,0,1,4,4,1,14,12,17,32,64,81,138,272,489,764,1548,2809,5062,
%T A247126 9420,17721,32712,60992,114105,213890,398784,747745,1401476,2624004,
%U A247126 4916369,9218118,17274340,32378521,60694768,113785984,213293721,399856922,749628208
%N A247126 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, U, X, N.
%H A247126 Alois P. Heinz, <a href="/A247126/b247126.txt">Table of n, a(n) for n = 0..1000</a>
%H A247126 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F A247126 G.f.: see Maple program.
%p A247126 gf:= -(x+1) *(4*x^19 -4*x^18 +8*x^17 -4*x^16 +12*x^15 -12*x^14 +9*x^13 -5*x^12 -2*x^10 +5*x^9 -6*x^8 +10*x^7 -10*x^6 +8*x^5 -7*x^4 +4*x^3 -3*x^2 +3*x-1) / (4*x^23 +8*x^22 +12*x^21 +32*x^20 +8*x^19 +6*x^18 -15*x^17 -22*x^16 -9*x^15 -9*x^14 +13*x^13 +4*x^12 +22*x^11 -15*x^10 +x^9 -9*x^8 -x^7 +3*x^6 +3*x^5 +3*x^4 -2*x^3 -2*x+1):
%p A247126 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A247126 seq(a(n), n=0..50);
%Y A247126 Cf. A174249, A233427, A234931, A077909, A247127.
%K A247126 nonn
%O A247126 0,5
%A A247126 _Alois P. Heinz_, Nov 19 2014