A239266 - OEIS

%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