A029595 Theta series of quadratic form (or lattice) with Gram matrix [ 1, 0, 0; 0, 2, 1; 0, 1, 3 ].

1, 2, 2, 8, 10, 0, 4, 12, 10, 6, 2, 16, 16, 8, 4, 4, 26, 4, 10, 32, 0, 8, 12, 12, 20, 2, 4, 32, 36, 8, 0, 24, 26, 8, 12, 8, 30, 16, 4, 24, 10, 8, 8, 56, 32, 0, 20, 12, 32, 14, 2, 48, 40, 8, 16, 0, 20, 16, 20, 32, 12, 16, 8, 36, 58, 4, 8, 72, 20, 8, 0, 24, 50, 20, 12, 8, 64

Offset

0,2

Comments

This is the digonal C lattice (the classical holotype) of dimension 3.

Links

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

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

Formula

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = Pi^(3/4) * 2^(1/5) * Gamma(9/10) * Gamma(7/10) * (2+2/5*5^(1/2)) * (1/4*5^(1/2)-1/4) * (1/4*5^(1/2)+1/4) / Gamma(3/4)^3 / Gamma(4/5)^2 = A388375. - Simon Plouffe, Sep 15 2025

Example

1 + 2*q + 2*q^2 + 8*q^3 + 10*q^4 + 4*q^6 + 12*q^7 + 10*q^8 + 6*q^9 + 2*q^10 + ...

Crossrefs

Sequence in context: A137726 A121098 A121094 * A343447 A320138 A325102

Adjacent sequences: A029592 A029593 A029594 * A029596 A029597 A029598

Keyword

nonn

Author

N. J. A. Sloane

Status

approved