A239265 Number of domicule tilings of a 3 X 2n grid.

1, 5, 43, 451, 4945, 54685, 605707, 6710971, 74358721, 823915861, 9129240139, 101154812563, 1120826772817, 12419109262381, 137607593744107, 1524734943844939, 16894537473570817, 187196730554444581, 2074198005431257579, 22982759116542299875

Offset

0,2

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..950

Index entries for linear recurrences with constant coefficients, signature (13,-21,-3).

Formula

G.f.: -(x^2+8*x-1)/(3*x^3+21*x^2-13*x+1).

Example

a(1) = 5:
  +---+  +---+  +---+  +---+  +---+
  |o o|  |o o|  |o-o|  |o-o|  |o-o|
  | X |  || ||  |   |  |   |  |   |
  |o o|  |o o|  |o-o|  |o o|  |o o|
  |   |  |   |  |   |  || ||  | X |
  |o-o|  |o-o|  |o-o|  |o o|  |o o|
  +---+  +---+  +---+  +---+  +---+.

Maple

gf:= -(x^2+8*x-1)/(3*x^3+21*x^2-13*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Crossrefs

Even bisection of column k=3 of A239264.

Sequence in context: A156886 A112115 A350117 * A369023 A274666 A301976

Adjacent sequences: A239262 A239263 A239264 * A239266 A239267 A239268

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 13 2014

Status

approved