A239267 Number of domicule tilings of a 5 X 2n grid.

1, 21, 1563, 162409, 17508475, 1894621633, 205109410835, 22206188455913, 2404176415007051, 260291084969169553, 28180738494571199683, 3051022897700513626745, 330322812747235906893563, 35762812820215620676404385, 3871905699058282397207463923

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..450

Crossrefs

Even bisection of column k=5 of A239264.

Programs

Maple

gf:= -(2048*x^7 -7680*x^6 -25472*x^5 +42048*x^4 -18928*x^3 +2912*x^2 -124*x+1) / (16384*x^8 -58112*x^7 -180608*x^6 +352480*x^5 -201552*x^4 +46976*x^3 -4394*x^2 +145*x-1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Formula

G.f.: -(2048*x^7 -7680*x^6 -25472*x^5 +42048*x^4 -18928*x^3 +2912*x^2 -124*x+1) / (16384*x^8 -58112*x^7 -180608*x^6 +352480*x^5 -201552*x^4 +46976*x^3 -4394*x^2 +145*x-1).