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A220299 Number of ways to cut a 6 X n rectangle into rectangles with integer sides.

%I A220299 #13 Mar 16 2023 13:39:50
%S A220299 1,32,2864,314662,36911922,4427635270,535236230270,64878517290010,
%T A220299 7871769490695758,955411617212520670,115973945786899746170,
%U A220299 14078248409306427591814,1709004742525016740261850,207462778992946779638832746,25184765957310295151583128422
%N A220299 Number of ways to cut a 6 X n rectangle into rectangles with integer sides.
%H A220299 Alois P. Heinz, <a href="/A220299/b220299.txt">Table of n, a(n) for n = 0..200</a>
%H A220299 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 A220299 Joshua Smith and Helena Verrill, <a href="/A116694/a116694.pdf">On dividing rectangles into rectangles</a>
%F A220299 G.f.: see Maple program.
%p A220299 gf:= (916798938728006656*x^20 -3962057190907156288*x^19 +7644699117821849592*x^18 -8795707489604640136*x^17 +6787540243858479914*x^16 -3741365942249935792*x^15 +1530293206620422033*x^14 -475918767335413756*x^13
%p A220299 +114321113226304761*x^12 -21415445169034874*x^11 +3143712388922139*x^10 -361909626897452*x^9 +32569667881308*x^8 -2274379347082*x^7 +121717789540*x^6 -4898404600*x^5 +144102468*x^4 -2968032*x^3 +39908*x^2 -308*x +1)/
%p A220299 (3488260147244630016*x^20 -13785403213649739264*x^19 +24571927550599277952*x^18 -26305901575283773400*x^17 +18988035581731414180*x^16 -9828185761768234778*x^15
%p A220299 +3785664669818771697*x^14 -1111033817019987980*x^13 +252212834590208135*x^12 -44688005447169948*x^11 +6207093806210985*x^10 -676048684437666*x^9 +57526055007906*x^8 -3794064844276*x^7 +191447789306*x^6 -7247125678*x^5 +199881354*x^4 -3842502*x^3 +47924*x^2 -340*x +1):
%p A220299 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A220299 seq(a(n), n=0..20);
%Y A220299 Column m=6 of A116694.
%K A220299 nonn
%O A220299 0,2
%A A220299 _Alois P. Heinz_, Dec 10 2012