A029594 Theta series of quadratic form with Gram matrix [ 1, 0, 0; 0, 2, 0; 0, 0, 3 ].

1, 2, 2, 6, 6, 4, 12, 4, 2, 14, 0, 8, 18, 4, 12, 16, 6, 4, 14, 8, 12, 24, 12, 8, 12, 10, 0, 18, 12, 12, 36, 12, 2, 16, 12, 8, 42, 12, 12, 36, 0, 12, 0, 8, 24, 28, 24, 8, 18, 14, 14, 32, 12, 12, 48, 8, 12, 36, 0, 16, 48, 12, 12, 28, 6, 16, 36, 16, 12, 32, 24, 24, 14, 8, 0, 42, 24, 8

Offset

0,2

Comments

This is the digonal P 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

Euler transform of period 24 sequence [2, -1, 4, -4, 2, -4, 2, -2, 4, -1, 2, -5, 2, -1, 4, -2, 2, -4, 2, -4, 4, -1, 2, -3, ...]. - Michael Somos, Sep 20 2005

Expansion of eta(q^2)^3eta(q^4)^3eta(q^6)^5/(eta(q)eta(q^3)eta(q^8)eta(q^12))^2 in powers of q. - Michael Somos, Sep 20 2005

G.f.: theta_3(q)theta_3(q^2)theta_3(q^3).

Example

1 + 2*q + 2*q^2 + 6*q^3 + 6*q^4 + 4*q^5 + 12*q^6 + 4*q^7 + 2*q^8 + 14*q^9 + ...

Mathematica

s = EllipticTheta[3, 0, q] EllipticTheta[3, 0, q^2] EllipticTheta[3, 0, q^3] + O[q]^80; CoefficientList[s, q] (* Jean-François Alcover, Nov 30 2015 *)

Prog

(PARI) a(n)=if(n<1, n==0, qfrep([1, 0, 0; 0, 2, 0; 0, 0, 3], n)[n]*2) /* Michael Somos, Sep 20 2005 */
(Sage)
Q = DiagonalQuadraticForm(ZZ, [1, 3, 2])
Q.representation_number_list(78) # Peter Luschny, Jun 25 2014

Crossrefs

Sequence in context: A184158 A060779 A324650 * A320191 A320190 A320189

Adjacent sequences: A029591 A029592 A029593 * A029595 A029596 A029597

Keyword

nonn

Author

N. J. A. Sloane

Status

approved