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A008806
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Expansion of (1+x^3)/((1-x^2)^2*(1-x^3)).
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2
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1, 0, 2, 2, 3, 4, 6, 6, 9, 10, 12, 14, 17, 18, 22, 24, 27, 30, 34, 36, 41, 44, 48, 52, 57, 60, 66, 70, 75, 80, 86, 90, 97, 102, 108, 114, 121, 126, 134, 140, 147, 154, 162, 168, 177, 184, 192, 200, 209, 216, 226, 234, 243, 252, 262, 270, 281, 290, 300, 310, 321
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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) = (16*A131713(n) +29 +24*n +6*n^2 +27*(-1)^n)/72.
G.f.: (1 -x +x^2)/( (1+x)*(1+x+x^2)*(1-x)^3 ). (End)
a(n) = floor((6*n^2+24*n+61+27*(-1)^n)/72). - Tani Akinari, Jul 24 2013
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MAPLE
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seq(coeff(series((1+x^3)/((1-x^2)^2*(1-x^3)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019
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MATHEMATICA
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CoefficientList[Series[(1+x^3)/((1-x^2)^2*(1-x^3)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 1, 0, -1, -1, 1}, {1, 0, 2, 2, 3, 4}, 70] (* G. C. Greubel, Sep 12 2019 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^3)/((1-x^2)^2*(1-x^3)) )); // G. C. Greubel, Sep 12 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^3)/((1-x^2)^2*(1-x^3))).list()
(GAP) a:=[1, 0, 2, 2, 3, 4];; for n in [7..70] do a[n]:=a[n-1]+a[n-2]-a[n-4]-a[n-5]+a[n-6]; od; a; # G. C. Greubel, Sep 12 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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EXTENSIONS
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STATUS
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approved
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