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A247124 Number of tilings of a 5 X n rectangle using n pentominoes of shapes I, U, X.

%I A247124 #17 Feb 06 2017 18:39:36
%S A247124 1,1,1,2,3,8,14,21,37,63,122,221,374,656,1147,2066,3699,6477,11407,
%T A247124 20099,35656,63323,111775,197352,348556,616560,1091570,1929721,
%U A247124 3410509,6028021,10658114,18851012,33331681,58927069,104177155,184188343,325686763,575858676
%N A247124 Number of tilings of a 5 X n rectangle using n pentominoes of shapes I, U, X.
%H A247124 Alois P. Heinz, <a href="/A247124/b247124.txt">Table of n, a(n) for n = 0..1000</a>
%H A247124 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F A247124 G.f.: see Maple program.
%e A247124 a(4) = 3:
%e A247124 ._______.   ._______.   ._______.
%e A247124 | | | | |   | | ._. |   | ._. | |
%e A247124 | | | | |   | |_| |_|   |_| |_| |
%e A247124 | | | | |   | |_. ._|   |_. ._| |
%e A247124 | | | | |   | | |_| |   | |_| | |
%e A247124 |_|_|_|_|   |_|_____|   |_____|_|  .
%p A247124 gf:= -(x-1)^2 *(x^4+x^3+x^2+x+1)^2 /
%p A247124      (x^15 +x^13 +x^11 -3*x^10 -2*x^8 -2*x^6 +6*x^5 +x^3 +x-1):
%p A247124 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A247124 seq(a(n), n=0..50);
%Y A247124 Cf. A174249, A233427, A247125, A247268, A264812.
%K A247124 nonn
%O A247124 0,4
%A A247124 _Alois P. Heinz_, Nov 19 2014