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A008798
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Molien series for group [2,5]+ = 225.
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1
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1, 0, 2, 0, 3, 1, 5, 2, 7, 3, 10, 5, 13, 7, 16, 10, 20, 13, 24, 16, 29, 20, 34, 24, 39, 29, 45, 34, 51, 39, 58, 45, 65, 51, 72, 58, 80, 65, 88, 72, 97, 80, 106, 88, 115, 97, 125, 106, 135, 115, 146, 125, 157, 135, 168, 146, 180, 157, 192, 168, 205, 180, 218, 192, 231, 205, 245, 218, 259
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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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G.f.: (1+x^6)/((1-x^2)^2*(1-x^5)).
a(n) = (17 + 6*n + 2*n^2 + 5*(-1)^n*(3 + 2*n) + 8*A080891(n+4))/40.
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MAPLE
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A080891 := proc(n) op((n mod 5)+1, [0, 1, -1, -1, 1]) ; end proc:
A008798 := proc(n) 17/40+3*n/20+n^2/20+(-1)^n*(3/8+n/4) +A080891(n+4)/5; end proc:
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MATHEMATICA
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CoefficientList[Series[(1+x^6)/((1-x^2)^2*(1-x^5)), {x, 0, 70}], x] (* G. C. Greubel, Sep 12 2019 *)
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PROG
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(PARI) my(x='x+O('x^70)); Vec((1+x^6)/((1-x^2)^2*(1-x^5))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^6)/((1-x^2)^2*(1-x^5)) )); // G. C. Greubel, Sep 12 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^6)/((1-x^2)^2*(1-x^5))).list()
(GAP) a:=[1, 0, 2, 0, 3, 1, 5, 2, 7];; for n in [10..70] do a[n]:=2*a[n-2]-a[n-4]+a[n-5]-2*a[n-7]+a[n-9]; od; a; # G. C. Greubel, Sep 12 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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EXTENSIONS
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STATUS
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approved
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