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A008446 Theta series of A_6 lattice. 5
1, 42, 210, 350, 882, 1050, 1750, 2100, 3570, 3066, 5250, 5124, 7350, 7350, 10500, 8064, 14322, 12600, 15330, 15750, 22050, 16814, 25620, 22260, 29750, 25242, 36750, 28700, 44100, 35364, 40320, 42000, 57330, 42700, 63000, 50442, 64386, 57540, 78750, 56448 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.

LINKS

Table of n, a(n) for n=0..39.

G. Nebe and N. J. A. Sloane, Home page for this lattice

EXAMPLE

1 + 42*q^2 + 210*q^4 + 350*q^6 + 882*q^8 + 1050*q^10 + 1750*q^12 + 2100*q^14 + 3570*q^16 + 3066*q^18 + 5250*q^20 + 5124*q^22 + 7350*q^24 + 7350*q^26 + 10500*q^28 + 8064*q^30 + 14322*q^32 + 12600*q^34 + 15330*q^36 + 15750*q^38 + 22050*q^40 + 16814*q^42 + 25620*q^44 + ...

MATHEMATICA

terms = 40; f[q_] = LatticeData["A6", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; DeleteCases[CoefficientList[s, q^(1/2) ] // Round, 0][[1 ;; terms]] (* Jean-Fran├žois Alcover, Jul 04 2017 *)

PROG

(MAGMA) L:=Lattice("A", 6); T1<q> := ThetaSeries(L, 120);

CROSSREFS

Sequence in context: A299817 A236278 A236271 * A255424 A122232 A193392

Adjacent sequences:  A008443 A008444 A008445 * A008447 A008448 A008449

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)