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A005813
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Molien series for 6-dimensional complex representation of double cover of J2.
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1
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1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2, 3, 1, 4, 2, 5, 5, 7, 4, 10, 8, 12, 12, 16, 13, 24, 21, 27, 27, 35, 34, 48, 45, 54, 57, 72, 70, 90, 88, 104, 112, 132, 132, 159, 162, 188, 199, 228, 230, 270, 281, 316, 333, 373, 384, 441, 458, 506, 532, 590, 613
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refs;
listen;
history;
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internal format)
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OFFSET
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0,13
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REFERENCES
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J. H. Conway and N. J. A. Sloane, circa 1977.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 1, 0, 1, 0, 0, -1, -1, -1, 0, -1, 0, 1, 0, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 1, 0, -1, 0, -1, -1, -1, 0, 0, 1, 0, 1, 1, 0, 0, -1).
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FORMULA
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a(n) ~ 1/2268000*n^5 + 1/151200*n^4 + 17/453600*n^3 (sequence without interleaved zeros). - Ralf Stephan, Apr 29 2014
G.f.: (1 -x^3 -x^4 +x^10 +x^11 +x^12 +x^16 -x^19 -x^23 +x^26 +x^30 +x^31 +x^32 -x^38 -x^39 +x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)). - G. C. Greubel, Feb 06 2020
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MAPLE
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# p/q = 1 +x^12 +x^20 +2*x^24 +x^28 +..., where
p := x^140 +x^110 +x^108 +x^106 +2*x^104 +2*x^102 +3*x^100 +3*x^98 +3*x^96 +3*x^94 +4*x^92 +4*x^90 +4*x^88 +4*x^86 +4*x^84 +4*x^82 +4*x^80 +4*x^78 +3*x^76 +4*x^74 +3*x^72 +4*x^70 +3*x^68 +4*x^66 +3*x^64 +4*x^62 +4*x^60 +4*x^58 +4*x^56 +4*x^54 +4*x^52 +4*x^50 +4*x^48 +3*x^46 +3*x^44 +3*x^42 +3*x^40 +2*x^38 +2*x^36 +x^34 +x^32 +x^30 +1;
q := (1-x^12)*(1-x^20)*(1-x^24)*(1-x^28)*(1-x^30)*(1-x^32);
seq(coeff(series(p/q, x, 2*n+1), x, 2*n), n=0..60);
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MATHEMATICA
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CoefficientList[Series[(1-x^3-x^4+x^10+x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)), {x, 0, 60}], x] (* G. C. Greubel, Feb 06 2020 *)
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PROG
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(PARI) Vec( (1-x^3-x^4+x^10+x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) +O('x^60) ) \\ G. C. Greubel, Feb 06 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x^3-x^4+x^10 +x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) )); // G. C. Greubel, Feb 06 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x^3-x^4+x^10+x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) ).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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