A029680 Theta series of quadratic form with Gram matrix [ 4, 2, 2; 2, 4, 1; 2, 1, 6 ].

1, 0, 6, 4, 4, 0, 14, 4, 6, 8, 2, 0, 20, 8, 12, 4, 16, 0, 26, 0, 0, 8, 8, 4, 42, 0, 20, 16, 12, 8, 0, 8, 14, 16, 20, 4, 36, 0, 20, 8, 6, 8, 52, 4, 8, 0, 12, 12, 52, 8, 6, 16, 24, 8, 46, 0, 20, 8, 20, 8, 16, 8, 20, 12, 28, 0, 64, 12, 16, 32, 0, 8, 58, 8, 20, 4, 16, 8, 60, 0, 0, 24, 44, 4, 40, 0, 20

Offset

0,3

Comments

This is the digonal F lattice (the even holotype) of dimension 3.

Links

John Cannon, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = coefficient of q^2n in theta3(q)*theta3(q^3)*theta3(q^5). Theta series of even sublattice of Z+sqrt(3)Z+sqrt(5)Z - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 07 2002 [corrected by Michael Somos, Apr 05 2012]

Example

1 + 6*x^2 + 4*x^3 + 4*x^4 + 14*x^6 + 4*x^7 + 6*x^8 + 8*x^9 + 2*x^10 + ...
1 + 6*q^4 + 4*q^6 + 4*q^8 + 14*q^12 + 4*q^14 + 6*q^16 + 8*q^18 + 2*q^20 + ...

Prog

(PARI) {a(n) = if( n<1, n==0, qfrep( [ 4, 2, 2; 2, 4, 1; 2, 1, 6], n, 1)[n] * 2 )} /* Michael Somos, Apr 05 2012 */

Crossrefs

Sequence in context: A099404 A095156 A198550 * A201285 A317127 A195359

Adjacent sequences: A029677 A029678 A029679 * A029681 A029682 A029683

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved