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%I A237356 #16 Nov 05 2020 06:07:43
%S A237356 1,29,1065,41097,1602289,62603505,2447085377,95662064129,
%T A237356 3739717169185,146197357313057,5715321341103969,223430193355808865,
%U A237356 8734601289109031137,341463519887132765409,13348901883923975256545,521851299448684501083617,20400837546324144424724449,797534035150318477886048225,31178158042817899845549718497
%N A237356 The number of tilings of the 3 X 4 X (2n) room with 1 X 2 X 2 boxes.
%C A237356 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 A237356 Vincenzo Librandi, <a href="/A237356/b237356.txt">Table of n, a(n) for n = 0..200</a>
%H A237356 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. (44).
%H A237356 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (55,-700,3186,-5180,2640).
%F A237356 G.f.: (1-2*x)*(-120*x^3+122*x^2-24*x+1) / ( (1-x) *(2640*x^4-2540*x^3+646*x^2-54*x+1) ) .
%p A237356 A237356 := proc(n)
%p A237356         (1-2*x)*(-120*x^3+122*x^2-24*x+1) / ( (1-x) *(2640*x^4-2540*x^3+646*x^2-54*x+1) ) ;
%p A237356         coeftayl(%,x=0,n) ;
%p A237356 end proc:
%p A237356 seq(A237356(n),n=0..20) ;
%t A237356 CoefficientList[Series[(1 - 2 x) (-120 x^3 + 122 x^2 - 24 x + 1)/((1 - x) (2640 x^4 - 2540 x^3 + 646 x^2 - 54 x + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 08 2014 *)
%Y A237356 Cf. A001045 (2 X 2 X n rooms), A083066 (2 X 3 X n rooms).
%K A237356 nonn,easy
%O A237356 0,2
%A A237356 _R. J. Mathar_, Feb 07 2014

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