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%I #13 Feb 06 2017 18:33:22
%S 1,0,0,1,0,2,1,0,4,5,38,22,13,90,144,457,408,386,1267,2230,5912,6481,
%T 7098,18896,35433,79634,101232,127501,288304,546652,1113907,1560356,
%U 2148298,4408181,8335234,15954116,23827541,35011426,67591204,126376945,232719926
%N Number of tilings of a 5 X n rectangle using n pentominoes of shapes Y, U, X.
%H Alois P. Heinz, <a href="/A247268/b247268.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.
%e a(3) = 1, a(5) = 2:
%e ._____. ._________. ._________.
%e | ._. | |_. .___| | | |___. ._|
%e |_| |_| | |_| |_. | | ._| |_| |
%e |_. ._| , | |_. ._| | | |_. ._| |
%e | |_| | | ._|_| |_| |_| |_|_. |
%e |_____| |_|_______| |_______|_| .
%p gf:= -(x^40 +12*x^39 +36*x^38 -5*x^36 -2*x^35 +12*x^34 +54*x^33 +4*x^32 -21*x^31 -23*x^30 +4*x^29 +20*x^28 +4*x^27 -4*x^25 -7*x^24 -6*x^23 -3*x^22 +33*x^21 -7*x^20 -10*x^19 -12*x^18 -9*x^17 +12*x^16 +16*x^15 +3*x^14 -2*x^13 -2*x^12 -2*x^11 -3*x^10 +5*x^9 -2*x^6 -7*x^5 -x^4 +1) /
%p (x^43 +12*x^42 +36*x^41 -3*x^40 -29*x^39 -58*x^38 +12*x^37 +67*x^36 +4*x^35 -123*x^34 -99*x^33 +8*x^32 +23*x^31 -145*x^30 -52*x^29 -52*x^28 -35*x^27 -112*x^26 -99*x^25 -28*x^24 -7*x^23 -15*x^22 -99*x^21 -42*x^20 +22*x^19 +36*x^18 +26*x^17 -4*x^16 +6*x^15 +31*x^14 +5*x^13 +11*x^12 +14*x^11 +23*x^10 -5*x^9 -7*x^8 -x^7 +2*x^6 +9*x^5 +x^4 +x^3 -1):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..60);
%Y Cf. A174249, A233427, A247124, A247125.
%K nonn
%O 0,6
%A _Alois P. Heinz_, Nov 30 2014
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