A346159 Number of n-dimensional representations of the group SU(3).

1, 1, 1, 3, 3, 3, 8, 8, 9, 17, 19, 21, 35, 39, 44, 68, 79, 87, 127, 145, 162, 228, 261, 291, 395, 451, 506, 665, 760, 850, 1096, 1254, 1400, 1765, 2016, 2249, 2800, 3188, 3556, 4356, 4953, 5522, 6688, 7581, 8447, 10123, 11464, 12747, 15141, 17094, 18997, 22395

Offset: 0

Author

Michel Marcus, Jul 08 2021

Keywords

• nonn

Links

• Kathrin Bringmann and Johann Franke, An asymptotic formula for the number of n-dimensional representations of SU(3), arXiv:2107.03261 [math.RT], 2021.
• Dan Romik, On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function, arXiv:1503.03776 [math.NT], 2015-2016.

Crossrefs

Cf. A107985 (as a rectangular array).

Programs

PARI

fij(lim) = my(imax = ceil((sqrt(8*lim+1)-1)/2), list=List()); for (i=1, imax, for (j=1, imax, if ((p=i*j*(i+j)/2) <= lim, listput(list, p)))); list;
lista(nn) = my(v=fij(nn), x='x+O('x^nn), w=Vec(prod(k=1, #v, 1/(1-x^v[k])))); vector(nn, k, w[k]);

Formula

G.f.: Product_{j,k>=1} 1/(1-x^(j*k*(j+k)/2)).