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A007478 Dimension of primitive Vassiliev knot invariants of order n.
(Formerly M0688)
4
1, 1, 1, 1, 2, 3, 5, 8, 12, 18, 27, 39, 55 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

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

LINKS

Table of n, a(n) for n=0..12.

D. Bar-Natan, On the Vassiliev Knot Invariants, Topology 34 (1995) 423-472.

D. Bar-Natan, Bibliography of Vassiliev Invariants.

Birman, Joan S., New points of view in knot theory (amstex), Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 253-287.

D. J. Broadhurst, Conjectured enumeration of Vassiliev invariants.

S. Chmutov and S. Duzhin, A lower bound for the number of Vassiliev knot invariants, Topology and its Applications, Volume 92, Number 3, 14 April 1999, pp. 201-223(23).

Jan Kneissler, The number of primitive Vassiliev invariants of degree up to 12

T. Ohtsuki (ed.), Problems on invariants of knots and 3-manifolds, arXiv:math/0406190 [math.GT], (2004); see Table 2 on p.407.

Index entries for sequences related to knots

FORMULA

Broadhurst gives a conjectured g.f.

Lim [n -> infinity] a(n) = n log n [Chmutov and Duzhin] - Jonathan Vos Post, Jul 24 2008

CROSSREFS

Cf. A014605, A050504.

Sequence in context: A136275 A328170 A078408 * A014605 A232477 A232478

Adjacent sequences:  A007475 A007476 A007477 * A007479 A007480 A007481

KEYWORD

hard,more,nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Next term is at least 78 (Jan Kneissler jk(AT)math.uni-bonn.de 9/97)

STATUS

approved

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Last modified December 11 07:38 EST 2019. Contains 329914 sequences. (Running on oeis4.)