A230059 Conjectural number of irreducible zeta values of weight 2*n+1 and depth three.

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, 56, 60, 65

Offset

1,6

Comments

a(n) corresponds to the value predicted by the Broadhurst-Kreimer conjecture.

Is this sequence the same as A340445? - R. J. Mathar, Jan 26 2021

Links

Table of n, a(n) for n=1..29.

A. B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998), no. 4, 497-516.

A. B. Goncharov, The dihedral Lie algebras and Galois symmetries of p_1^l(P^1 - 0, infinity and N-th roots of unity), arXiv:math/0009121 [math.AG], 2000; Duke Math. J. 110 (2001), 397-487.

K. Ihara, M. Kaneko, and D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compos. Math. 142 (2006), no 2, p. 307-338.

Formula

Conjecturally, a(n) = [((n-1)^2-1)/12] for n > 1.

Conjecturally, g.f.: x^5*(1+x-x^2)/((1-x)*(1-x^2)*(1-x^3)).

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.

Crossrefs

Sequence in context: A056902 A089676 A334653 * A340445 A302486 A266745

Adjacent sequences: A230056 A230057 A230058 * A230060 A230061 A230062

Keyword

nonn,more

Author

Samuel Baumard, Oct 08 2013

Status

approved