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A220297 Number of ways to cut a 4 X n rectangle into rectangles with integer sides.

%I A220297 #25 Mar 18 2023 14:47:26
%S A220297 1,8,148,3164,70878,1613060,36911922,846280548,19415751782,
%T A220297 445550465628,10225294476962,234675373081668,5385967300825942,
%U A220297 123612245431357148,2837003283963428562,65111601723938370628,1494366038587416919782,34296959750113321113308
%N A220297 Number of ways to cut a 4 X n rectangle into rectangles with integer sides.
%H A220297 Alois P. Heinz, <a href="/A220297/b220297.txt">Table of n, a(n) for n = 0..300</a>
%H A220297 David A. Klarner and Spyros S. Magliveras, <a href="https://doi.org/10.1016/S0195-6698(88)80062-3">The number of tilings of a block with blocks</a>, European Journal of Combinatorics 9 (1988), 317-330.
%H A220297 Joshua Smith and Helena Verrill, <a href="/A116694/a116694.pdf">On dividing rectangles into rectangles</a>
%H A220297 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (44,-645,4280,-13840,20980,-11680).
%F A220297 G.f.: see Maple program.
%e A220297 a(1) = 8:
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%e A220297   | |  | |  |_|  | |  |_|  | |  |_|  |_|
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%e A220297   |_|  |_|  |_|  |_|  |_|  |_|  |_|  |_|
%e A220297 .
%p A220297 gf:= (3832*x^6 -8492*x^5 +6722*x^4 -2468*x^3 +441*x^2 -36*x+1) / (11680*x^6 -20980*x^5 +13840*x^4 -4280*x^3 +645*x^2 -44*x+1):
%p A220297 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A220297 seq(a(n), n=0..20);
%Y A220297 Column m=4 of A116694.
%K A220297 nonn,easy
%O A220297 0,2
%A A220297 _Alois P. Heinz_, Dec 10 2012