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A023902 Theta series of A_11 lattice. 13

%I

%S 1,132,2970,19800,66462,194832,420684,881760,1511730,2770284,4134240,

%T 6754968,9491130,14310120,18773964,27609648,34253142,47864520,

%U 58862870,78974808,93470652

%N Theta series of A_11 lattice.

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

%t 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 *)

%o (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))

%o 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)))

%o 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

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)