cp's OEIS Frontend

A237357 The number of tilings of the 3 X 3 X (2n) room with 1 X 2 X 3 boxes.

%I A237357 #19 Mar 20 2024 13:52:14
%S A237357 1,6,64,616,5936,57408,554624,5359040,51781696,500337216,4834483264,
%T A237357 46712942656,451361370176,4361255727168,42140406169664,
%U A237357 407179478511680,3934350491492416,38015456589811776,367322368167936064,3549233239845138496,34294281215843786816
%N A237357 The number of tilings of the 3 X 3 X (2n) room with 1 X 2 X 3 boxes.
%C A237357 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 A237357 Vincenzo Librandi, <a href="/A237357/b237357.txt">Table of n, a(n) for n = 0..200</a>
%H A237357 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 A237357 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,22,36).
%F A237357 G.f.: (1-x)/(-22*x^2-7*x-36*x^3+1).
%p A237357 A237357 := proc(n)
%p A237357     (1-x)/ (-22*x^2-7*x-36*x^3+1) ;
%p A237357     coeftayl(%,x=0,n) ;
%p A237357 end proc:
%p A237357 seq(A237357(n),n=0..20) ;
%t A237357 CoefficientList[Series[(1 - x)/(-22 x^2 - 7 x - 36 x^3 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 08 2014 *)
%t A237357 LinearRecurrence[{7,22,36},{1,6,64},30] (* _Harvey P. Dale_, Mar 20 2024 *)
%Y A237357 Cf. A000079 (2 X 2 X n rooms), A103143 (2 X 3 X n rooms).
%K A237357 nonn,easy
%O A237357 0,2
%A A237357 _R. J. Mathar_, Feb 07 2014