cp's OEIS Frontend

A226370 Number of tilings of a 6 X n rectangle using integer-sided square tiles of area > 1.

%I A226370 #19 Sep 05 2021 21:59:27
%S A226370 1,0,1,1,3,2,7,7,16,19,40,51,98,136,245,355,617,923,1560,2386,3962,
%T A226370 6147,10085,15804,25716,40569,65652,104040,167738,266634,428798,
%U A226370 683021,1096560,1749127,2804915,4478363,7175960,11464553,18360713,29346366,46982101
%N A226370 Number of tilings of a 6 X n rectangle using integer-sided square tiles of area > 1.
%H A226370 Alois P. Heinz, <a href="/A226370/b226370.txt">Table of n, a(n) for n = 0..1000</a>
%H A226370 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,2,0,1).
%F A226370 G.f.: 1/(1-x^2-x^3-2*x^4-x^6).
%F A226370 a(n) = a(n-2)+a(n-3)+2*a(n-4)+a(n-6) for n>5, a(0) = a(2) = a(3) = 1, a(1) = 0, a(4) = 3, a(5) = 2.
%e A226370 a(4) = 3:
%e A226370 ._._._._.   ._._._._.   ._._._._.
%e A226370 |       |   |   |   |   |   |   |
%e A226370 |       |   |___|___|   |___|___|
%e A226370 |       |   |       |   |   |   |
%e A226370 |_______|   |       |   |___|___|
%e A226370 |   |   |   |       |   |   |   |
%e A226370 |___|___|   |_______|   |___|___|
%p A226370 a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,
%p A226370     `if`(i=6, [1, 0, 2, 1, 1, 0][j], 0)))^n. <<1, 0, 1, 1, 3, 2>>)[1, 1]:
%p A226370 seq(a(n), n=0..60);
%Y A226370 Column k=6 of A226206.
%K A226370 nonn,easy
%O A226370 0,5
%A A226370 _Alois P. Heinz_, Jun 05 2013