cp's OEIS Frontend

A234312 Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, X.

%I A234312 #26 May 28 2019 08:12:19
%S A234312 1,0,2,0,4,2,8,8,16,24,36,64,88,160,224,392,576,960,1472,2368,3728,
%T A234312 5888,9376,14720,23488,36896,58752,92544,146944,232064,367680,581632,
%U A234312 920448,1457152,2305024,3649664,5773312,9140224,14460928,22890496,36221184,57327616
%N A234312 Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, X.
%H A234312 Alois P. Heinz, <a href="/A234312/b234312.txt">Table of n, a(n) for n = 0..1000</a>
%H A234312 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A234312 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,0,2)
%F A234312 G.f.: -1/(2*x^5+2*x^2-1).
%F A234312 a(n) = 2*(a(n-2)+a(n-5)) for n>4, a(1)=a(3)=0, a(0)=1, a(2)=2, a(4)=4.
%e A234312 a(4) = 4:
%e A234312 ._______.  ._______.  ._______.  ._______.
%e A234312 |_. |_. |  | ._| ._|  |_. | ._|  | ._|_. |
%e A234312 | | | | |  | | | | |  | | | | |  | | | | |
%e A234312 | | | | |  | | | | |  | | | | |  | | | | |
%e A234312 | |_| |_|  |_| |_| |  | |_|_| |  |_| | |_|
%e A234312 |___|___|  |___|___|  |___|___|  |___|___|.
%e A234312 a(5) = 2:
%e A234312 ._________.  ._________.
%e A234312 | | ._____|  |_____. | |
%e A234312 | |_| |_. |  | ._| |_| |
%e A234312 | |_. ._| |  | |_. ._| |
%e A234312 |___|_| | |  | | |_|___|
%e A234312 |_______|_|  |_|_______|.
%p A234312 a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,
%p A234312           <0|0|0|0|1>, <2|0|0|2|0>>^n)[5, 5]:
%p A234312 seq(a(n), n=0..50);
%t A234312 LinearRecurrence[{0, 2, 0, 0, 2}, {1, 0, 2, 0, 4}, 50] (* _Jean-François Alcover_, May 28 2019 *)
%Y A234312 Cf. A077909, A174249, A233427, A234931, A247125, A264812.
%K A234312 nonn
%O A234312 0,3
%A A234312 _Alois P. Heinz_, Dec 23 2013