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A023902 Theta series of A_11 lattice. 14
1, 132, 2970, 19800, 66462, 194832, 420684, 881760, 1511730, 2770284, 4134240, 6754968, 9491130, 14310120, 18773964, 27609648, 34253142, 47864520, 58862870, 78974808, 93470652, 125490024, 143483340, 186539760, 214957644, 271553700, 304365600 (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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

MATHEMATICA

terms = 21; f[q_] = LatticeData["A11", "ThetaSeriesFunction"][-I Log[q] / Pi]; s = Series[f[q], {q, 0, 2 terms}]; CoefficientList[s, q^2][[1 ;; terms]] (* Jean-Fran├žois Alcover, Jul 04 2017 *)

PROG

(PARI) theta3(k, n, prec, f, m)=f=polcyclo(n); 1+sum(m=1, sqrtint(prec), Mod(x^(m*k%n)+x^(m*(n-k)%n), f)*q^sqr(m))+O(q^(prec+1))

aaa(n, prec, k, m)=sum(k=0, n-1, theta3(k, n, prec)^n)/n/(1+2*sum(m=1, sqrtint(floor(prec/n)), q^(n*sqr(m)))+O(q^(prec+1)))

doit(m, prec)=subst(lift(aaa(m+1, prec)), x, 0) \\ gives theta series of A_m to order "prec"; code from Robert.Harley(AT)inria.fr

CROSSREFS

Sequence in context: A220996 A254646 A242147 * A240270 A168180 A236260

Adjacent sequences:  A023899 A023900 A023901 * A023903 A023904 A023905

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Sean A. Irvine, Jun 12 2019

STATUS

approved

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Last modified April 14 05:41 EDT 2021. Contains 342946 sequences. (Running on oeis4.)