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%I #12 Nov 23 2018 06:44:21
%S 1,1,11,43,280,1563,9415,55553,331133,1968400,11716601,69716257,
%T 414898579,2469046811,14693544104,87442204835,520375602855,
%U 3096794588441,18429266069421,109673987617376,652678415082545,3884139865306433,23114817718082715,137558073518189643
%N Number of domicule tilings of a 4 X n grid.
%C 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.
%H Alois P. Heinz, <a href="/A239266/b239266.txt">Table of n, a(n) for n = 0..1000</a>
%F 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).
%e a(2) = 11:
%e +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
%e |o o| |o o| |o o| |o-o| |o o| |o-o| |o o| |o o| |o-o| |o-o| |o-o|
%e | X | | X | | X | | | || || | | || || || || | | | | | |
%e |o o| |o o| |o o| |o o| |o o| |o-o| |o o| |o o| |o-o| |o-o| |o o|
%e | | | | | | | X | | | | | | | | | | | | | || ||
%e |o o| |o o| |o-o| |o o| |o o| |o o| |o o| |o-o| |o o| |o-o| |o o|
%e | X | || || | | | | | X | | X | || || | | || || | | | |
%e |o o| |o o| |o-o| |o-o| |o o| |o o| |o o| |o-o| |o o| |o-o| |o-o|
%e +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+.
%p 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):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..30);
%Y Column k=4 of A239264.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Mar 13 2014
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