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A023917 Theta series of A*_5 lattice. 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 23 06:59 EDT 2024. Contains 374544 sequences. (Running on oeis4.)