A007473 Dimension of space of Vassiliev knot invariants of order n.

1, 1, 2, 3, 6, 10, 19, 33, 60, 104, 184, 316, 548

Offset: 0

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• nice

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Dror Bar-Natan, On the Vassiliev Knot Invariants, Topology 34 (1995) 423-472.
• Dror Bar-Natan, Bibliography of Vassiliev Invariants
• D. J. Broadhurst, Conjectured enumeration of Vassiliev invariants, arXiv:q-alg/9709031, 1997.
• Maksim Karev, On the primitive subspace of Lando framed graph bialgebra, arXiv:2307.00468 [math.CO], 2023.
• Jan Kneissler, The number of primitive Vassiliev invariants of degree up to 12, arXiv:q-alg/9706022, 1997.
• Eric Weisstein's World of Mathematics, Vassiliev Invariant.
• Index entries for sequences related to knots

Crossrefs

Cf. A007293 (first differences), A007478, A014595 (conjectured continuation).

Formula

G.f.: Product_{ m >= 1 } (1-y^m)^(-A007478(m)). - Andrey Zabolotskiy, Sep 19 2017

Broadhurst gives a conjectured explicit g.f. (different from A014595).

Extensions

Description corrected by Sergei Duzhin, Aug 29 2000