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A008751
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Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)).
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1
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1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 19, 23, 26, 31, 35, 40, 45, 51, 56, 63, 69, 76, 83, 91, 98, 107, 115, 124, 133, 143, 152, 163, 173, 184, 195, 207, 218, 231, 243, 256, 269, 283, 296, 311, 325, 340, 355
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = floor((n^2 - 2*n + 18)/6) for n>2.
a(n) = a(n-2) + a(n-3) - a(n-5) + 2.
a(n) = A008747(n-2) + 2 for n>2. (End)
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MATHEMATICA
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CoefficientList[Series[(1+x^8)/((1-x)(1-x^2)(1-x^3)), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 25 2012 *)
Join[{1, 1, 2}, Floor[((Range[3, 50] -1)^2 +17)/6]] (* G. C. Greubel, Aug 04 2019 *)
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PROG
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(PARI) my(x='x+O('x^50)); Vec((1+x^8)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^8)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^8)/((1-x)*(1-x^2)*(1-x^3))).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) Concatenation([1, 1, 2], List([3..50], n-> Int(((n-1)^2 +17)/6))); # G. C. Greubel, Aug 04 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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