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%I #20 Feb 07 2017 17:01:58
%S 1,0,2,6,14,32,102,238,652,1696,4480,11658,30870,80644,212292,556858,
%T 1463390,3840686,10090218,26490280,69575414,182693434,479789138,
%U 1259906496,3308668718,8688615148,22817011182,59918425698,157349755400,413208421354,1085110433096
%N Number of tilings of a 4 X n rectangle using L and Z tetrominoes.
%H Alois P. Heinz, <a href="/A232497/b232497.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetromino">Tetromino</a>
%F G.f.: -(x^6-x^5-2*x^4+x^3+3*x^2-1) / (2*x^12 +4*x^10 +6*x^8 +6*x^7 +13*x^6 +13*x^5 -2*x^4 -7*x^3 -5*x^2+1).
%e a(3) = 6:
%e ._._._. ._._._. ._._._. ._._._. ._._._. ._._._.
%e | .___| |___. | | |_. | | ._| | | .___| |___. |
%e |_| ._| |_. |_| |_. | | | | ._| |_| | | | | |_|
%e |___| | | |___| | |_|_| |_|_| | | ._| | | |_. |
%e |_____| |_____| |_____| |_____| |_|___| |___|_|.
%p a:= n-> coeff(series(-(x^6-x^5-2*x^4+x^3+3*x^2-1)/
%p (2*x^12+4*x^10+6*x^8+6*x^7+13*x^6+13*x^5-2*x^4-7*x^3-5*x^2+1),
%p x, n+1), x, n);
%p seq(a(n), n=0..40);
%Y Cf. A084480, A174248, A226322, A233139, A233191, A233266.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Nov 24 2013
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