A022067 - OEIS

%I #17 Jul 14 2021 02:46:40

%S 1,0,28,0,364,0,2912,16384,16044,0,64792,229376,200928,0,503360,

%T 1490944,1089452,0,2186940,6193152,4196920,0,7544992,19382272,

%U 12547808,0,19975256,50692096,31553344,0,48484800,116523008,70439852,0,99602104,241106944,142487436

%N Theta series of D*_14 lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

%H Andy Huchala, <a href="/A022067/b022067.txt">Table of n, a(n) for n = 0..20000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds14.html">Home page for this lattice</a>

%e G.f. = 1 + 28*q^2 + 364*q^4 + ...

%o (Sage)

%o L = [1, 0, 28, 0]

%o M = ModularForms(Gamma1(4),7)

%o bases = [_.q_expansion(20) for _ in M.integral_basis()]

%o f = sum(x*y for (x,y) in zip(bases,L)); list(f) # _Andy Huchala_, Jul 13 2021

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, Jul 13 2021