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
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.
Comments