cp's OEIS Frontend

A226369 Number of tilings of a 5 X n rectangle using integer-sided square tiles of area > 1.

%I A226369 #18 Sep 05 2021 21:59:02
%S A226369 1,0,0,0,0,1,2,0,0,0,1,4,4,0,0,1,6,12,8,0,1,8,24,32,16,1,10,40,80,80,
%T A226369 33,12,60,160,240,193,78,84,280,560,673,464,240,448,1120,1793,1810,
%U A226369 1168,928,2016,4033,5396,4788,3264,3872,8065,13462,15580,12840,10400
%N A226369 Number of tilings of a 5 X n rectangle using integer-sided square tiles of area > 1.
%H A226369 Alois P. Heinz, <a href="/A226369/b226369.txt">Table of n, a(n) for n = 0..1000</a>
%H A226369 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,2).
%F A226369 G.f.: 1/(1-x^5-2*x^6).
%F A226369 a(n) = a(n-5)+2*a(n-6) for n>5, a(0) = a(5) = 1, a(1) = a(2) = a(3) = a(4) = 0.
%e A226369 a(6) = 2:
%e A226369 ._._._._._._.    ._._._._._._.
%e A226369 |     |     |    |   |   |   |
%e A226369 |     |     |    |___|___|___|
%e A226369 |_____|_____|    |     |     |
%e A226369 |   |   |   |    |     |     |
%e A226369 |___|___|___|    |_____|_____|
%p A226369 a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,
%p A226369     `if`(i=6, [2, 1, 0$4][j], 0)))^n. <<1, [0$4][], 1>>)[1, 1]:
%p A226369 seq(a(n), n=0..70);
%Y A226369 Column k=5 of A226206.
%K A226369 nonn,easy
%O A226369 0,7
%A A226369 _Alois P. Heinz_, Jun 05 2013