A029671 Theta series of quadratic form with Gram matrix [ 2, 1, 0; 1, 4, 1; 0, 1, 4 ].

1, 2, 6, 8, 6, 8, 4, 8, 18, 10, 4, 20, 16, 0, 12, 16, 14, 16, 18, 12, 24, 8, 12, 32, 12, 14, 2, 32, 20, 16, 16, 8, 42, 16, 8, 40, 30, 16, 28, 0, 12, 12, 24, 32, 40, 24, 8, 40, 32, 14, 30, 32, 0, 40, 16, 16, 36, 24, 20, 44, 40, 8, 28, 40, 30, 4, 16, 44, 48, 16, 16, 40, 54, 12, 28, 40, 24

Offset

0,2

Comments

This is the monoclinic P 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

Example

1 + 2*x + 6*x^2 + 8*x^3 + 6*x^4 + 8*x^5 + 4*x^6 + 8*x^7 + 18*x^8 + ...
1 + 2*q^2 + 6*q^4 + 8*q^6 + 6*q^8 + 8*q^10 + 4*q^12 + 8*q^14 + 18*q^16 + 10*q^18 + ...

Prog

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

Crossrefs

Sequence in context: A065129 A074758 A228163 * A278081 A329592 A154970

Adjacent sequences: A029668 A029669 A029670 * A029672 A029673 A029674

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved