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A008649
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Molien series of 3 X 3 upper triangular matrices over GF( 3 ).
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3
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1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 7, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18, 18, 22, 22, 22, 26, 26, 26, 30, 30, 30, 35, 35, 35, 40, 40, 40, 45, 45, 45, 51, 51, 51, 57, 57, 57, 63, 63, 63, 70, 70, 70, 77, 77, 77, 84, 84, 84, 92, 92, 92, 100, 100, 100
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OFFSET
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0,4
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COMMENTS
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REFERENCES
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D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1).
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FORMULA
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G.f.: 1/((1-x)*(1-x^3)*(1-x^9)).
a(n) = floor((6*(floor(n/3) +1)*(3*floor(n/3) -n +1) +n^2 +13*n +58)/54). - Tani Akinari, Jul 12 2013
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MAPLE
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1/((1-x)*(1-x^3)*(1-x^9)): seq(coeff(series(%, x, n+1), x, n), n=0..70);
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MATHEMATICA
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CoefficientList[Series[1/((1-x)*(1-x^3)*(1-x^9)), {x, 0, 70}], x] (* G. C. Greubel, Sep 06 2019 *)
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PROG
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(PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^3)*(1-x^9))) \\ G. C. Greubel, Sep 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^3)*(1-x^9)) )); // G. C. Greubel, Sep 06 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P(1/((1-x)*(1-x^3)*(1-x^9))).list()
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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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