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