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%I #19 Mar 20 2024 13:52:14
%S 1,6,64,616,5936,57408,554624,5359040,51781696,500337216,4834483264,
%T 46712942656,451361370176,4361255727168,42140406169664,
%U 407179478511680,3934350491492416,38015456589811776,367322368167936064,3549233239845138496,34294281215843786816
%N The number of tilings of the 3 X 3 X (2n) room with 1 X 2 X 3 boxes.
%C The count compiles all arrangements without respect to symmetry: Stacks that are equivalent after rotations or flips through any of the 3 axes or 3 planes are counted with multiplicity.
%H Vincenzo Librandi, <a href="/A237357/b237357.txt">Table of n, a(n) for n = 0..200</a>
%H R. J. Mathar, <a href="http://arxiv.org/abs/1406.7788">Tilings of rectangular regions by rectangular tiles: counts derived from transfer matrices</a>, arXiv:1406.7788 [math.CO], eq. (57).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,22,36).
%F G.f.: (1-x)/(-22*x^2-7*x-36*x^3+1).
%p A237357 := proc(n)
%p (1-x)/ (-22*x^2-7*x-36*x^3+1) ;
%p coeftayl(%,x=0,n) ;
%p end proc:
%p seq(A237357(n),n=0..20) ;
%t CoefficientList[Series[(1 - x)/(-22 x^2 - 7 x - 36 x^3 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 08 2014 *)
%t LinearRecurrence[{7,22,36},{1,6,64},30] (* _Harvey P. Dale_, Mar 20 2024 *)
%Y Cf. A000079 (2 X 2 X n rooms), A103143 (2 X 3 X n rooms).
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Feb 07 2014
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