Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Sep 24 2023 10:23:45
%S 1,0,0,0,198506,163840,20662272,45481984,745402040,1904738304,
%T 13582315520,32267304960,152158214640,321893203968,1194291679232,
%U 2263580016640,7176091448362
%N Theta series of the canonical laminated lattice LAMBDA_29.
%C Theta series is an element of the space of modular forms on Gamma_0(16) of weight 29/2 and dimension 30 over the integers.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 179.
%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.2307/2007025">Laminated lattices</a>, Annals of Math., 116 (1982), pp. 593-620. A revised version appears as Chapter 6 of "Sphere Packings, Lattices and Groups" by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.
%H J. H. Conway and N. J. A. Sloane, <a href="/A005135/a005135.png">The "shower" showing containments among the laminated lattices up to dimension 48</a> (Fig 3 from the Annals paper, also Fig. 6.1 in the Sphere packing book).
%H G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA29.html">Home page for this lattice</a>
%H <a href="/index/La#laminated">Index entries for sequences related to laminated lattices</a>
%e G.f.: 1 + 198506*q^8 + 163840*q^10 + ...
%o (Magma)
%o L := Lattice("Lambda", 29);
%o T<q> := ThetaSeries(L, 14);
%o C := Coefficients(T);
%o [C[2*i-1] : i in [1..8]];
%Y Cf. A005135, A023942, A008408.
%K nonn,more
%O 0,5
%A _Andy Huchala_, Jun 27 2021
%E a(14)-a(16) from _Robin Visser_, Sep 24 2023