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A008761
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Expansion of (1+x^18)/((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, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 38, 41, 46, 51, 56, 61, 68, 73, 80, 87, 94, 101, 110, 117, 126, 135, 144, 153, 164, 173, 184, 195, 206, 217, 230, 241, 254, 267, 280, 293, 308
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OFFSET
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0,3
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LINKS
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MAPLE
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seq(coeff(series((1+x^18)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 09 2019
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MATHEMATICA
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Join[{1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19}, LinearRecurrence[{1, 1, 0, -1, -1, 1}, {21, 24, 27, 30, 33, 38}, 47]] (* G. C. Greubel, Aug 09 2019 *)
CoefficientList[Series[(1+x^18)/((1-x)(1-x^2)(1-x^3)), {x, 0, 70}], x] (* Harvey P. Dale, Jun 06 2021 *)
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PROG
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(PARI) my(x='x+O('x^60)); Vec((1+x^18)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^18)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 09 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^18)/((1-x)*(1-x^2)*(1-x^3))).list()
(GAP) a:=[21, 24, 27, 30, 33, 38];; for n in [7..60] do a[n]:=a[n-1]+a[n-2]-a[n-4]-a[n-5]+a[n-6]; od; Concatenation([1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19], a); # G. C. Greubel, Aug 09 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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