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URL: https://oeis.org/A239266

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A239266
Number of domicule tilings of a 4 X n grid.
2
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.
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 13 2014
STATUS
approved