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%I #22 Feb 07 2017 17:03:27
%S 1,0,0,0,2,4,8,18,44,104,242,564,1320,3090,7228,16904,39538,92484,
%T 216328,506002,1183564,2768424,6475506,15146580,35428712,82869778,
%U 193837148,453396168,1060519538,2480615780,5802302024,13571915922,31745486700,74254506984
%N Number of tilings of a 4 X n rectangle using T and Z tetrominoes.
%H Alois P. Heinz, <a href="/A233139/b233139.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetromino">Tetromino</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,2).
%F G.f.: (x^3+2*x-1) / (2*x^4+x^3+2*x-1).
%F a(n) = 2*a(n-1)+a(n-3)+2*a(n-4) for n>3, a(0)=1, a(1)=a(2)=a(3)=0.
%e a(5) = 4:
%e ._____.___. .___._____. ._._____._. ._._____._.
%e |_. ._| ._| |_. |_. ._| | |_. ._| | | |_. ._| |
%e | |_|___| | | |___|_| | | ._|_|_. | | ._|_|_. |
%e | ._| |_. | | ._| |_. | |_| |_. |_| |_| ._| |_|
%e |_|_____|_| |_|_____|_| |_____|___| |___|_____|.
%p a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|1|0|2>>^n.
%p <<1, 0, 0, 0>>)[1, 1]:
%p seq(a(n), n=0..40);
%Y Cf. A084480, A174248, A226322, A230031, A232497, A233191, A233266.
%K nonn,easy
%O 0,5
%A _Alois P. Heinz_, Dec 04 2013
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