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A237358
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The number of tilings of the 3 X 4 X n room with 1 X 2 X 3 boxes.
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2
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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
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0,3
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COMMENTS
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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.
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LINKS
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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).
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MAPLE
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(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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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