A023917 Theta series of A*_5 lattice.

1, 0, 0, 0, 0, 12, 0, 0, 30, 20, 0, 0, 30, 0, 0, 0, 0, 120, 0, 0, 132, 60, 0, 0, 90, 0, 0, 0, 0, 180, 0, 0, 270, 180, 0, 0, 140, 0, 0, 0, 0, 480, 0, 0, 420, 132, 0, 0, 270, 0, 0, 0, 0, 420, 0, 0, 600, 420, 0, 0, 360, 0, 0, 0, 0, 960, 0, 0, 840, 360, 0, 0, 330, 0, 0, 0, 0

Offset

0,6

Comments

Expansion of Ahlgren's F_6(q^2).

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.

Links

John Cannon, Table of n, a(n) for n = 0..10000

S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc., 128 (2000), 1333-1338.

G. Nebe and N. J. A. Sloane, Home page for this lattice

Example

1 + 12*q^5 + 30*q^8 + 20*q^9 + 30*q^12 + 120*q^17 + 132*q^20 + 60*q^21 + 90*q^24 + 180*q^29 + 270*q^32 + 180*q^33 + 140*q^36 + 480*q^41 + 420*q^44 + 132*q^45 + 270*q^48 + 420*q^53 + 600*q^56 + 420*q^57 + 360*q^60 + O(q^61)

Mathematica

terms = 77; phi[q_] := EllipticTheta[3, 0, q]; F6[q_] := (1/32)*(-3*phi[Sqrt[q]]^5 + 5*phi[Sqrt[q]]^3*phi[Sqrt[q^3]]^2 + 15*phi[Sqrt[q]] * phi[Sqrt[q^3]]^4 + (15*phi[Sqrt[q^3]]^6)/phi[Sqrt[q]]); s = Simplify[F6[q^2], q>0]; s = s + O[q]^(2 terms); CoefficientList[s, q][[1 ;; terms]] (* Jean-François Alcover, Jul 04 2017 *)

Prog

(Magma) L:=Lattice("A", 5); D:=Dual(L); T1<q> := ThetaSeries(D, 120);

Crossrefs

Sequence in context: A360223 A270256 A072837 * A359001 A347802 A230926

Adjacent sequences: A023914 A023915 A023916 * A023918 A023919 A023920

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved