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

0,2

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).

Formula

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

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 *)

Crossrefs

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

Sequence in context: A067447 A083225 A320528 * A230282 A186668 A025609

Adjacent sequences: A237354 A237355 A237356 * A237358 A237359 A237360

Keyword

nonn,easy

Author

R. J. Mathar, Feb 07 2014

Status

approved