A237358 - OEIS

A237358

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

1, 1, 11, 64, 296, 1716, 9123, 48761, 264457, 1420548, 7652666, 41237256, 222050029, 1196138637, 6442843111, 34702528552, 186921714672, 1006820870616, 5423072856651, 29210535955209, 157337764568209, 847474515870020, 4564784961695166, 24587476389796440

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OFFSET

0,3

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.

The rational generating function is the main body of the Maple program.

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. (58).

Index entries for linear recurrences with constant coefficients, signature (2, 14, 42, -42, -237, -504, -103, 487, 1012, 448, -306, -74, -915, 450, -873, -54, 162).

MAPLE

A237358 := proc(n)

(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) ;

coeftayl(%, x=0, n) ;

end proc:

seq(A237358(n), n=0..20) ;

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A362164 A357959 A285361 * A250604 A233164 A215445

Adjacent sequences: A237355 A237356 A237357 * A237359 A237360 A237361

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Feb 07 2014

STATUS

approved