A005813 Molien series for 6-dimensional complex representation of double cover of J2.

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

Offset

0,13

References

J. H. Conway and N. J. A. Sloane, circa 1977.

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

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).

Index entries for Molien series

Formula

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

Maple

#  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);

Mathematica

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 *)

Prog

(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)
def A005813_list(prec):
    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()
A005813_list(60) # G. C. Greubel, Feb 06 2020

Crossrefs

Sequence in context: A263136 A080018 A079686 * A049262 A374748 A145201

Adjacent sequences: A005810 A005811 A005812 * A005814 A005815 A005816

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved