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

0,4

Links

Table of n, a(n) for n=0..51.

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.

Formula

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

Prog

(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]);

Crossrefs

Cf. A107985 (as a rectangular array).

Sequence in context: A111521 A177937 A029628 * A241739 A226509 A329694

Adjacent sequences: A346156 A346157 A346158 * A346160 A346161 A346162

Keyword

nonn

Author

Michel Marcus, Jul 08 2021

Status

approved