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%I #13 Jan 13 2017 13:50:51
%S 1,2,9,45,201,1062,5564,28859,152012,799387,4202165,22117465,
%T 116385352,612443308,3223118545,16961953022,89264218645,469766599585,
%U 2472212575433,13010374123502,68468999197712,360328057238019,1896278913278432,9979444454056631
%N Number of tilings of a 2 X 2 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.
%H Alois P. Heinz, <a href="/A233505/b233505.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (x^17 +3*x^16 -x^15 -5*x^14 +8*x^13 -8*x^12 -22*x^10 -20*x^9 -62*x^8 -20*x^7 -42*x^6 +18*x^5 +19*x^3 +x^2 +3*x -1) / (-x^20 -2*x^19 +2*x^18 +9*x^17 -12*x^16 +27*x^15 +41*x^14 +66*x^13 +62*x^12 +184*x^11 +76*x^10 +156*x^9 -92*x^8 +20*x^7 -141*x^6 +28*x^5 -62*x^4 +19*x^3 +5*x -1).
%p a:= n-> coeff(series((x^17 +3*x^16 -x^15 -5*x^14 +8*x^13 -8*x^12 -22*x^10 -20*x^9 -62*x^8 -20*x^7 -42*x^6 +18*x^5 +19*x^3 +x^2 +3*x -1)/(-x^20 -2*x^19 +2*x^18 +9*x^17 -12*x^16 +27*x^15 +41*x^14 +66*x^13 +62*x^12 +184*x^11 +76*x^10 +156*x^9 -92*x^8 +20*x^7 -141*x^6 +28*x^5 -62*x^4 +19*x^3 +5*x -1), x, n+1), x, n):
%p seq(a(n), n=0..40);
%Y Cf. A000931, A129682, A219866, A219867, A233313, A233506, A233507, A233509.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Dec 11 2013
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