%I #19 Jan 26 2021 11:44:52
%S 0,0,0,0,1,2,2,4,5,6,8,10,11,14,16,18,21,24,26,30,33,36,40,44,47,52,
%T 56,60,65
%N Conjectural number of irreducible zeta values of weight 2*n+1 and depth three.
%C a(n) corresponds to the value predicted by the Broadhurst-Kreimer conjecture.
%C Is this sequence the same as A340445? - _R. J. Mathar_, Jan 26 2021
%H A. B. Goncharov, <a href="http://dx.doi.org/10.4310/MRL.1998.v5.n4.a7">Multiple polylogarithms, cyclotomy and modular complexes</a>, Math. Res. Lett. 5 (1998), no. 4, 497-516.
%H A. B. Goncharov, <a href="https://arxiv.org/abs/math/0009121">The dihedral Lie algebras and Galois symmetries of p_1^l(P^1 - 0, infinity and N-th roots of unity)</a>, arXiv:math/0009121 [math.AG], 2000; Duke Math. J. 110 (2001), 397-487.
%H K. Ihara, M. Kaneko, and D. Zagier, <a href="https://doi.org/10.1112/S0010437X0500182X">Derivation and double shuffle relations for multiple zeta values</a>, Compos. Math. 142 (2006), no 2, p. 307-338.
%F Conjecturally, a(n) = [((n-1)^2-1)/12] for n > 1.
%F Conjecturally, g.f.: x^5*(1+x-x^2)/((1-x)*(1-x^2)*(1-x^3)).
%F Conjecturally, a(n) = if(n<5, 0, (1/2)*(-2*a(n-3) - 4*a(n-2) - 4*a(n-1) + n^2 - 5*n + 2)). - _Jean-François Alcover_, Feb 23 2019.
%K nonn,more
%O 1,6
%A _Samuel Baumard_, Oct 08 2013