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A247117 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape I.

%I A247117 #19 Feb 06 2017 18:26:15
%S A247117 1,1,1,1,1,8,17,28,41,56,144,317,609,1060,1716,3324,6713,13188,24624,
%T A247117 43620,80464,153645,296025,562097,1037921,1920661,3600832,6820873,
%U A247117 12920804,24211457,45173688,84493668,158848825,299451277,562923960,1055117520,1976475968
%N A247117 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape I.
%H A247117 Alois P. Heinz, <a href="/A247117/b247117.txt">Table of n, a(n) for n = 0..1000</a>
%H A247117 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F A247117 G.f.: see Maple program.
%p A247117 gf:= -(x^10+x^8-x^6-2*x^5-x^4-x^3+1) *(x-1)^4 *(x^4+x^3+x^2+x+1)^4 / (x^35 +x^33 -2*x^31 -7*x^30 -2*x^29 -6*x^28 +x^27 +9*x^26 +22*x^25 +8*x^24 +15*x^23 -4*x^22 -15*x^21 -39*x^20 -12*x^19 -20*x^18 +6*x^17 +10*x^16 +45*x^15 +8*x^14 +19*x^13 -4*x^12 -4*x^11 -33*x^10 -6*x^9 -10*x^8 +x^7 -3*x^6 +12*x^5 +x^3 +x-1):
%p A247117 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A247117 seq(a(n), n=0..50);
%Y A247117 Cf. A174249, A233427, A003520 (5 X n), A247218 (15 X n).
%Y A247117 Column k=5 of A250662.
%K A247117 nonn,easy
%O A247117 0,6
%A A247117 _Alois P. Heinz_, Nov 19 2014