A220298 - OEIS

%I #19 Mar 16 2023 13:39:29

%S 1,16,650,31484,1613060,84231996,4427635270,233276449488,

%T 12300505521832,648782777031100,34223109012944482,1805323555104984956,

%U 95234889270955121716,5023877415526067785580,265022449692240368203598,13980623266954069411358904

%N Number of ways to cut a 5 X n rectangle into rectangles with integer sides.

%H Alois P. Heinz, <a href="/A220298/b220298.txt">Table of n, a(n) for n = 0..200</a>

%H 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 Joshua Smith and Helena Verrill, <a href="/A116694/a116694.pdf">On dividing rectangles into rectangles</a>

%F G.f.: see Maple program.

%e a(1) = 16:

%e   ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._.

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%e   | | | | | | |_| | | | | |_| | | |_| | | |_| |_| | | |_| |_| |_|

%e   | | | | | | | | |_| | | | | |_| | | |_| |_| | | |_| |_| |_| |_|

%e   |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_|

%e .

%p gf:= (39672144*x^10 -110891556*x^9 +124284414*x^8 -74544838*x^7 +26669637*x^6 -5961522*x^5 +841659*x^4 -73608*x^3 +3769*x^2 -100*x+1)/

%p (135762480*x^10 -326041524*x^9 +320708934*x^8 -170972730*x^7 +54776249*x^6 -11002298*x^5 +1395665*x^4 -109292*x^3 +4975*x^2 -116*x +1):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..20);

%Y Column m=5 of A116694.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Dec 10 2012