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A008718
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Expansion of g.f.: (1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).
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8
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1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 9, 10, 11, 12, 15, 16, 19, 20, 23, 26, 29, 30, 36, 39, 42, 45, 51, 54, 60, 63, 69, 75, 81, 84, 94, 100, 106, 112, 122, 128, 138, 144, 154, 164, 174, 180, 195, 205, 215, 225, 240, 250, 265, 275, 290, 305, 320, 330, 351, 366
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OFFSET
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0,5
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COMMENTS
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Molien series for genus-2 weight enumerators of binary self-dual codes is (1+x^18)/((1-x^2)*(1-x^8)*(1-x^12)*(1-x^24)). Exponents have been divided by 2 to get the sequence.
Or, Molien series for 4-dimensional representation of 2.{3,4,3}. This is the real 4-dimensional Clifford group of genus 2 and order 2304.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,-1,0,-1,1,0,0,0,1,-1,0,-1,0,1,0,1,-1).
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FORMULA
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G.f.: ( 1-x^3+x^6 ) / ( (1-x+x^2) *(x^4-x^2+1) *(1+x)^2 *(x^2+1)^2 *(1+x+x^2)^2 *(x-1)^4 ). - R. J. Mathar, Dec 18 2014
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MAPLE
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(1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)); seq(coeff(series(%, x, n+1), x, n), n = 0..65); # modified by G. C. Greubel, Sep 09 2019
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MATHEMATICA
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CoefficientList[Series[(1+x^9)/((1-x)(1-x^4)(1-x^6)(1-x^12)), {x, 0, 65}], x] (* Harvey P. Dale, Apr 01 2011 *)
LinearRecurrence[{1, 0, 1, 0, -1, 0, -1, 1, 0, 0, 0, 1, -1, 0, -1, 0, 1, 0, 1, -1}, {1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 9, 10, 11, 12, 15, 16, 19, 20}, 65] (* Ray Chandler, Jul 16 2015 *)
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PROG
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(PARI) my(x='x+O('x^65)); Vec((1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)) )); // G. C. Greubel, Sep 09 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12))).list()
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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