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A099560
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a(n) = Sum_{k=0..floor(n/3)} C(n-2k,k-1).
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3
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0, 0, 0, 1, 1, 1, 3, 4, 5, 9, 13, 18, 28, 41, 59, 88, 129, 188, 277, 406, 594, 872, 1278, 1872, 2745, 4023, 5895, 8641, 12664, 18559, 27201, 39865, 58424, 85626, 125491, 183915, 269542, 395033, 578948, 848491, 1243524, 1822472, 2670964, 3914488
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OFFSET
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0,7
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LINKS
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FORMULA
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G.f.: x^3/((1-x^3)(1-x-x^3)).
a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-6).
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MATHEMATICA
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Table[Sum[Binomial[n-2k, k-1], {k, 0, Floor[n/3]}], {n, 0, 50}] (* or *) LinearRecurrence[{1, 0, 2, -1, 0, -1}, {0, 0, 0, 1, 1, 1}, 50] (* Harvey P. Dale, May 25 2014 *)
CoefficientList[Series[x^3/((1 - x^3) (1 - x - x^3)), {x, 0, 50}], x] (* G. C. Greubel, Apr 28 2017 *)
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PROG
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(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(x^3/((1-x^3)*(1-x-x^3)))) \\ G. C. Greubel, Apr 28 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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