cp's OEIS Frontend

A237358 The number of tilings of the 3 X 4 X n room with 1 X 2 X 3 boxes.

%I A237358 #19 Apr 17 2024 15:06:39
%S A237358 1,1,11,64,296,1716,9123,48761,264457,1420548,7652666,41237256,
%T A237358 222050029,1196138637,6442843111,34702528552,186921714672,
%U A237358 1006820870616,5423072856651,29210535955209,157337764568209,847474515870020,4564784961695166,24587476389796440
%N A237358 The number of tilings of the 3 X 4 X n room with 1 X 2 X 3 boxes.
%C A237358 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.
%C A237358 The rational generating function is the main body of the Maple program.
%H A237358 Vincenzo Librandi, <a href="/A237358/b237358.txt">Table of n, a(n) for n = 0..200</a>
%H A237358 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. (58).
%H A237358 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (2, 14, 42, -42, -237, -504, -103, 487, 1012, 448, -306, -74, -915, 450, -873, -54, 162).
%p A237358 A237358 := proc(n)
%p A237358     (1-x)*(1+x)*(1-3*x)*(3*x^2+2*x+1)*(1-x^2-7*x^3+9*x^6)/
%p A237358     (504*x^6 +306*x^11 +1 -1012*x^9 +103*x^7 -2*x +54*x^16 -162*x^17
%p A237358     -450*x^14 +74*x^12 -14*x^2 -487*x^8 -42*x^3 -448*x^10 +915*x^13
%p A237358     +237*x^5 +873*x^15 +42*x^4) ;
%p A237358     coeftayl(%,x=0,n) ;
%p A237358 end proc:
%p A237358 seq(A237358(n),n=0..20) ;
%t A237358 CoefficientList[Series[(1 - x) (1 + x) (1 - 3 x) (3 x^2 + 2 x + 1) (1 - x^2 - 7 x^3 + 9 x^6)/(504 x^6 + 306 x^11 + 1 - 1012 x^9 + 103 x^7 - 2 x + 54 x^16 - 162 x^17 - 450 x^14 + 74 x^12 - 14 x^2 - 487 x^8 - 42 x^3 - 448 x^10 + 915 x^13 + 237 x^5 + 873 x^15 + 42 x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 08 2014 *)
%Y A237358 Cf. A000079 (2 X 2 X n rooms), A103143 (2 X 3 X n rooms).
%K A237358 nonn,easy
%O A237358 0,3
%A A237358 _R. J. Mathar_, Feb 07 2014