|
%I #26 Jun 13 2015 00:54:40
%S 1,0,3,6,19,48,141,378,1063,2920,8115,22418,62123,171876,475919,
%T 1317250,3646681,10094356,27943739,77353070,214129845,592752572,
%U 1640859689,4542223926,12573787053,34806745800,96352029241,266721635838,738338745535,2043868995512
%N Number of tilings of a 4 X n rectangle using L tetrominoes and 2 X 2 tiles.
%H Alois P. Heinz, <a href="/A226322/b226322.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,6,4,0,-1,0,-3,-2,-4,0,-2).
%F G.f.: (x^6+2*x^2-1) / (-2*x^12 -4*x^10 -2*x^9 -3*x^8 -x^6 +4*x^4 +6*x^3 +5*x^2-1).
%e a(3) = 6:
%e ._____. ._____. .___._. ._.___. ._____. ._____.
%e | .___| |___. | | | | | | | |___. | | .___|
%e |_|_. | | ._|_| |___| | | |___| | |_| |_| |
%e | | | | | | | |___| |___| | |___| | | |___|
%e |___|_| |_|___| |_____| |_____| |_____| |_____|
%p a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,
%p [-2, 0, -4, -2, -3, 0, -1, 0, 4, 6, 5, 0][j], 0)))^(n+8).
%p <<-1, 0, 1/2, [0$5][], 1, 0, 3, 6>>)[1, 1]:
%p seq(a(n), n=0..40);
%t a[n_] := MatrixPower[ Table[ If[i+1 == j, 1, If[i == 12, {-2, 0, -4, -2, -3, 0, -1, 0, 4, 6, 5, 0}[[j]], 0]], {i, 1, 12}, {j, 1, 12}], n+8].{-1, 0, 1/2, 0, 0, 0, 0, 0, 1, 0, 3, 6} // First; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Dec 05 2013, after Maple *)
%Y Cf. A054854, A054856, A084480, A165716, A165791, A165799, A174248, A232497, A233191, A233266.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Jun 03 2013
|
