A239268 Number of domicule tilings of a 6 X n grid.

1, 1, 43, 451, 9415, 162409, 3037561, 55263473, 1017093992, 18633949879, 342050825969, 6273663002379, 115107979930355, 2111655465575629, 38740910476086035, 710728644139932355, 13038974254406437397, 239210680096992061776, 4388527184214799104521

Offset: 0

Author

Alois P. Heinz, Mar 13 2014

Keywords

• nonn
• easy

Comments

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..750

Crossrefs

Column k=6 of A239264.

Programs

Maple

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) /
(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):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Formula

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).