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A322496 Number of tilings of a 3 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.

%I A322496 #12 May 21 2020 04:26:33
%S A322496 1,1,3,8,18,44,107,257,621,1500,3620,8740,21101,50941,122983,296908,
%T A322496 716798,1730504,4177807,10086117,24350041,58786200,141922440,
%U A322496 342631080,827184601,1997000281,4821185163,11639370608,28099926378,67839223364,163778373107
%N A322496 Number of tilings of a 3 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.
%C A322496 The shapes of the tiles are:
%C A322496               ._.
%C A322496        ._.    | |
%C A322496   ._.  | |_.  | |_._.
%C A322496   |_|  |___|  |_____|  .
%H A322496 Alois P. Heinz, <a href="/A322496/b322496.txt">Table of n, a(n) for n = 0..1000</a>
%H A322496 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%H A322496 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,3,1).
%F A322496 G.f.: -1/((x^2+x+1)*(x^2+2*x-1)).
%F A322496 a(n) = 2*a(n-1) + a(n-2) + A049347(n). - _Greg Dresden_, May 18 2020
%e A322496 a(3) = 8:
%e A322496   ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.
%e A322496   |_|_|_|  | |_|_|  |_|_|_|  |_| |_|  |_|_|_|  |_| |_|  | |_|_|  | | |_|
%e A322496   |_|_|_|  |___|_|  | |_|_|  |_|___|  |_| |_|  | |___|  | |_|_|  | |___|
%e A322496   |_|_|_|  |_|_|_|  |___|_|  |_|_|_|  |_|___|  |___|_|  |_____|  |_____|  .
%p A322496 a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1|3|2|1>>^n)[4$2]:
%p A322496 seq(a(n), n=0..40);
%Y A322496 Column k=3 of A322494.
%K A322496 nonn,easy
%O A322496 0,3
%A A322496 _Alois P. Heinz_, Dec 12 2018