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A233247
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Expansion of ( 1-x^3-x^2 ) / ( (x^3-x^2-1)*(x^3+2*x^2+x-1) ).
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2
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1, 1, 1, 4, 9, 16, 36, 81, 169, 361, 784, 1681, 3600, 7744, 16641, 35721, 76729, 164836, 354025, 760384, 1633284, 3508129, 7535025, 16184529, 34762816, 74666881, 160376896, 344473600, 739894401, 1589218225, 3413480625, 7331811876, 15747991081, 33825095056
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OFFSET
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0,4
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COMMENTS
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a(n) is the number of tilings of a 3 X 2 X n room with bricks of 1 X 1 X 3 shape (and in that respect a generalization of A028447 which fills 3 X 2 X n rooms with bricks of 1 X 1 X 2 shape).
The inverse INVERT transform is 1, 0, 3, 2, 2, 4, 4, 6, 8, 10, .. , continued as in A068924.
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LINKS
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FORMULA
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MAPLE
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end proc:
# second Maple program:
a:= n-> (<<0|1|0>, <0|0|1>, <1|0|1>>^n)[3, 3]^2:
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MATHEMATICA
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Table[Sum[Binomial[n-2i, i], {i, 0, n/3}]^2, {n, 0, 50}] (* Wesley Ivan Hurt, Dec 06 2013 *)
LinearRecurrence[{1, 1, 3, 1, -1, -1}, {1, 1, 1, 4, 9, 16}, 40] (* Harvey P. Dale, Jan 14 2015 *)
CoefficientList[Series[(1-x^3-x^2)/((x^3-x^2-1)*(x^3+2*x^2+x-1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 29 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1-x^3-x^2)/((x^3-x^2-1)*(x^3+2*x^2+x-1))) \\ G. C. Greubel, Apr 29 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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