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%I #10 Feb 06 2017 18:55:30
%S 1,0,0,1,4,0,9,8,24,17,78,64,227,212,664,699,2004,2220,6033,7196,
%T 18112,22859,54882,72560,166251,229284,505632,721421,1540532,2264668,
%U 4702135,7092742,14376450,22165709,44024116,69154334,134973515,215459398,414268932
%N Number of tilings of a 5 X n rectangle using n pentominoes of shapes V, U, X, N.
%H Alois P. Heinz, <a href="/A247127/b247127.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.: see Maple program.
%p gf:= -(4*x^18 +4*x^17 -8*x^16 -3*x^15 -9*x^14 +2*x^13 -3*x^12 +5*x^11 -7*x^10 +x^9 -7*x^8 -x^6 -2*x^5 -x^3+1) / (32*x^26 +32*x^25 -32*x^24 +8*x^23 -120*x^22 +12*x^21 -124*x^20 +36*x^19 -123*x^18 +35*x^17 -106*x^16 +20*x^15 -62*x^14 -23*x^13 -22*x^12 -36*x^11 +5*x^10 -18*x^9 +13*x^8 -4*x^7 +8*x^6 +2*x^5 +4*x^4 +2*x^3-1):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..50);
%Y Cf. A174249, A233427, A247126.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Nov 19 2014
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