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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
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-François 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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Jun 12 2019
STATUS
approved

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Last modified July 14 12:15 EDT 2024. Contains 374318 sequences. (Running on oeis4.)