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A008817
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Expansion of (1+x^10)/((1-x)^2*(1-x^10)).
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10
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 97, 104, 111, 118, 125, 132, 139, 146, 153, 160, 169, 178, 187, 196, 205, 214, 223, 232, 241, 250, 261, 272, 283, 294, 305, 316, 327, 338, 349, 360
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,1,-2,1).
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FORMULA
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G.f.: (1+x^10)/((1-x)^2*(1-x^10)).
a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=5, a(5)=6, a(6)=7, a(7)=8, a(8)=9, a(9)=10, a(10)=13, a(11)=16, a(n) = 2*a(n-1) - a(n-2) + a(n-10) - 2*a(n-11) + a(n-12). - Harvey P. Dale, Jul 31 2014
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MAPLE
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seq(coeff(series((1+x^10)/((1-x)^2*(1-x^10)), x, n+1), x, n), n = 0..80); # G. C. Greubel, Sep 12 2019
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MATHEMATICA
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CoefficientList[Series[(1+x^10)/(1-x)^2/(1-x^10), {x, 0, 80}], x] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16}, 80] (* Harvey P. Dale, Jul 31 2014 *)
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PROG
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(PARI) my(x='x+O('x^80)); Vec((1+x^10)/((1-x)^2*(1-x^10))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^10)/((1-x)^2*(1-x^10)) )); // G. C. Greubel, Sep 12 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^10)/((1-x)^2*(1-x^10))).list()
(GAP) a:=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16];; for n in [13..80] do a[n]:=2*a[n-1]-a[n-2]+a[n-10]-2*a[n-11]+a[n-12]; 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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STATUS
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approved
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