A239266 Number of domicule tilings of a 4 X n grid.

1, 1, 11, 43, 280, 1563, 9415, 55553, 331133, 1968400, 11716601, 69716257, 414898579, 2469046811, 14693544104, 87442204835, 520375602855, 3096794588441, 18429266069421, 109673987617376, 652678415082545, 3884139865306433, 23114817718082715, 137558073518189643

Offset

0,3

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..1000

Formula

G.f.: -(x-1)*(x^3-x^2+5*x-1)/(5*x^6-11*x^5+30*x^4-30*x^3-2*x^2+7*x-1).

Example

a(2) = 11:
  +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
  |o o| |o o| |o o| |o-o| |o o| |o-o| |o o| |o o| |o-o| |o-o| |o-o|
  | X | | X | | X | |   | || || |   | || || || || |   | |   | |   |
  |o o| |o o| |o o| |o o| |o o| |o-o| |o o| |o o| |o-o| |o-o| |o o|
  |   | |   | |   | | X | |   | |   | |   | |   | |   | |   | || ||
  |o o| |o o| |o-o| |o o| |o o| |o o| |o o| |o-o| |o o| |o-o| |o o|
  | X | || || |   | |   | | X | | X | || || |   | || || |   | |   |
  |o o| |o o| |o-o| |o-o| |o o| |o o| |o o| |o-o| |o o| |o-o| |o-o|
  +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+.

Maple

gf:= -(x-1)*(x^3-x^2+5*x-1)/(5*x^6-11*x^5+30*x^4-30*x^3-2*x^2+7*x-1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Crossrefs

Column k=4 of A239264.

Sequence in context: A201714 A269422 A259798 * A259963 A201991 A010819

Adjacent sequences: A239263 A239264 A239265 * A239267 A239268 A239269

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 13 2014

Status

approved