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
KEYWORD
nonn
AUTHOR
STATUS
approved