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

1, 6, 64, 616, 5936, 57408, 554624, 5359040, 51781696, 500337216, 4834483264, 46712942656, 451361370176, 4361255727168, 42140406169664, 407179478511680, 3934350491492416, 38015456589811776, 367322368167936064, 3549233239845138496, 34294281215843786816

Offset: 0

Author

R. J. Mathar, Feb 07 2014

Keywords

• nonn
• easy

Comments

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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• R. J. Mathar, Tilings of rectangular regions by rectangular tiles: counts derived from transfer matrices, arXiv:1406.7788 [math.CO], eq. (57).
• Index entries for linear recurrences with constant coefficients, signature (7,22,36).

Crossrefs

Cf. A000079 (2 X 2 X n rooms), A103143 (2 X 3 X n rooms).

Programs

Maple

A237357 := proc(n)
    (1-x)/ (-22*x^2-7*x-36*x^3+1) ;
    coeftayl(%,x=0,n) ;
end proc:
seq(A237357(n),n=0..20) ;

Mathematica

CoefficientList[Series[(1 - x)/(-22 x^2 - 7 x - 36 x^3 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 08 2014 *)
LinearRecurrence[{7,22,36},{1,6,64},30] (* Harvey P. Dale, Mar 20 2024 *)

Formula

G.f.: (1-x)/(-22*x^2-7*x-36*x^3+1).