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A230059
Conjectural number of irreducible zeta values of weight 2*n+1 and depth three.
3
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
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
KEYWORD
nonn,more
AUTHOR
Samuel Baumard, Oct 08 2013
STATUS
approved