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