cp's OEIS Frontend

A128102 Number of 2 X 2 tiles in all tilings of a 4 X n rectangle with 1 X 1 and 2 X 2 square tiles.

%I A128102 #4 Sep 03 2016 09:24:56
%S A128102 0,0,5,14,69,224,805,2610,8545,27068,85209,264406,814509,2488536,
%T A128102 7558093,22827130,68625657,205455348,612884929,1822355742,5402974789,
%U A128102 15977195792,47135117493,138757706946,407679684497,1195641350700
%N A128102 Number of 2 X 2 tiles in all tilings of a 4 X n rectangle with 1 X 1 and 2 X 2 square tiles.
%C A128102 a(n)=Sum(k*A128101(n,k), k=0..2*floor(n/2)).
%D A128102 S. Heubach, Tiling an m X n area with squares of size up to k X k (m <=5), Congressus Numerantium 140 (1999), pp. 43-64.
%H A128102 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-16,-1,12,-4).
%F A128102 G.f.=z^2*(5-6z+3z^2)/(1-2z-3z^2+2z^3)^2.
%p A128102 g:=z^2*(5-6*z+3*z^2)/(1-2*z-3*z^2+2*z^3)^2: gser:=series(g,z=0,32): seq(coeff(gser,z,n),n=0..29);
%Y A128102 Cf. A128101.
%K A128102 nonn
%O A128102 0,3
%A A128102 _Emeric Deutsch_, Feb 19 2007