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%I #11 Aug 29 2015 02:15:12
%S 1,1,43,451,9415,162409,3037561,55263473,1017093992,18633949879,
%T 342050825969,6273663002379,115107979930355,2111655465575629,
%U 38740910476086035,710728644139932355,13038974254406437397,239210680096992061776,4388527184214799104521
%N Number of domicule tilings of a 6 X n grid.
%C A domicule is either a domino or it is formed by the union of two neighboring unit squares connected via their corners. In a tiling the connections of two domicules are allowed to cross each other.
%H Alois P. Heinz, <a href="/A239268/b239268.txt">Table of n, a(n) for n = 0..750</a>
%F G.f.: -(45*x^18 +330*x^17 -3649*x^16 +872*x^15 +13497*x^14 -31638*x^13 +33844*x^12 +87562*x^11 -231307*x^10 -22714*x^9 +206771*x^8 -57002*x^7 -8736*x^6 +7970*x^5 -2193*x^4 -364*x^3 +145*x^2 +10*x-1) / (585*x^20 +4335*x^19 -47413*x^18 +4273*x^17 +187195*x^16 -352817*x^15 +385178*x^14 +1070602*x^13 -2911442*x^12 -370773*x^11 +2929813*x^10 -729299*x^9 -407618*x^8 +200422*x^7 -19642*x^6 -15983*x^5 +4787*x^4 +563*x^3 -177*x^2 -11*x+1).
%p gf:= -(45*x^18 +330*x^17 -3649*x^16 +872*x^15 +13497*x^14 -31638*x^13 +33844*x^12 +87562*x^11 -231307*x^10 -22714*x^9 +206771*x^8 -57002*x^7 -8736*x^6 +7970*x^5 -2193*x^4 -364*x^3 +145*x^2 +10*x-1) /
%p (585*x^20 +4335*x^19 -47413*x^18 +4273*x^17 +187195*x^16 -352817*x^15 +385178*x^14 +1070602*x^13 -2911442*x^12 -370773*x^11 +2929813*x^10 -729299*x^9 -407618*x^8 +200422*x^7 -19642*x^6 -15983*x^5 +4787*x^4 +563*x^3 -177*x^2 -11*x+1):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..20);
%Y Column k=6 of A239264.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Mar 13 2014
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