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A219925 Number of tilings of a 6 X n rectangle using integer-sided square tiles.

%I A219925 #17 Sep 05 2021 18:21:12
%S A219925 1,1,13,60,348,1916,10668,59257,329350,1830234,10171315,56525022,
%T A219925 314128014,1745708992,9701463927,53914132251,299618062228,
%U A219925 1665073290365,9253344266757,51423790446062,285778433090830,1588162056821687,8825923956549044,49048479247236561
%N A219925 Number of tilings of a 6 X n rectangle using integer-sided square tiles.
%H A219925 Alois P. Heinz, <a href="/A219925/b219925.txt">Table of n, a(n) for n = 0..500</a>
%F A219925 G.f.: see Maple program.
%e A219925 a(2) = 13, because there are 13 tilings of a 6 X 2 rectangle using integer-sided square tiles:
%e A219925 ._._.  .___.  ._._.  ._._.  ._._.  ._._.
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%e A219925 |_|_|  |_|_|  |_|_|  |_|_|  |___|  |   |
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%e A219925 .___.  .___.  .___.  ._._.  ._._.  ._._.  .___.
%e A219925 |   |  |   |  |   |  |_|_|  |_|_|  |_|_|  |   |
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%e A219925 |   |  |_|_|  |_|_|  |___|  |___|  |   |  |   |
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%p A219925 gf:= -(2*x^9 +3*x^8 +2*x^7 -3*x^6 -7*x^5 -4*x^4 -3*x^3 +5*x^2 +2*x -1) / (2*x^15 +7*x^14 +12*x^13 +6*x^12 -18*x^11 -13*x^10 -8*x^9 -27*x^8 -32*x^7 +x^6 +40*x^5 +34*x^4 -3*x^3 -15*x^2 -3*x +1):
%p A219925 a:= n-> coeff (series (gf, x, n+1), x, n):
%p A219925 seq (a(n), n=0..40);
%Y A219925 Column k=6 of A219924.
%Y A219925 Cf. A226549.
%K A219925 nonn,easy
%O A219925 0,3
%A A219925 _Alois P. Heinz_, Dec 01 2012