A125564 Theta series of 5-dimensional lattice A_5^{+3}.

1, 0, 30, 30, 0, 132, 90, 0, 270, 140, 0, 420, 270, 0, 600, 360, 0, 840, 330, 0, 1092, 660, 0, 1200, 810, 0, 1500, 570, 0, 1980, 1020, 0, 2190, 1260, 0, 2280, 1100, 0, 2460, 1560, 0, 3360, 1620, 0, 3780, 1452, 0, 3360, 2190, 0, 3930, 2340, 0, 4620, 1710, 0, 5400, 2940

Offset: 0

Author

N. J. A. Sloane, Jan 31 2007

Keywords

• nonn

Examples

			1 + 30*q^4 + 30*q^6 + 132*q^10 + 90*q^12 + 270*q^16 + 140*q^18 + 420*q^22 + ...
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110 and 116.

Links

• John Cannon, Table of n, a(n) for n = 0..5000
• J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices I: Quadratic Forms of Small Determinant, Proc. Royal Soc. London, Series A, 418 (1988), 17-41.
• LMFDB, Integral lattice 5.162.12.1.1
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Crossrefs

Cf. A008445, A125561, A023917.

Programs

Mathematica

al[n_, l_, p_, nn_] := Sum[Exp[-2 Pi I k l/n] EllipticTheta[3, Pi k/n, q^p]^n, {k, n}] / n / Sum[q^(p n (m + l/n)^2), {m, -nn, nn}] + O[q]^nn;
as[n_, s_, nn_] := CoefficientList[FullSimplify[Normal@Sum[al[n, l, n/s, nn], {l, s, n, s}]], q];
as[6, 1, 30] (*A023917*)
as[6, 2, 30][[;; ;; 2]] (*this sequence*)
as[6, 3, 30] (*A125561*)
(* Andrey Zabolotskiy, Feb 17 2022 *)

Extensions

Typo in name corrected by Andrey Zabolotskiy, Feb 16 2022