

A029680


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


1



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
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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



