A014595 Conjectured dimensions of spaces of weight systems of chord diagrams.

1, 1, 2, 3, 6, 10, 19, 33, 60, 104, 184, 316, 548, 931, 1588, 2676, 4511, 7539, 12590, 20890, 34603, 57036, 93804, 153655, 251109, 408961, 664467, 1076398, 1739660, 2804166, 4510035, 7236242, 11585908, 18509442, 29511312, 46957178, 74575323, 118213424, 187052097, 295453415

Offset

0,3

Comments

First 13 terms agree with A007473, next terms obtained from A014605.

Links

Table of n, a(n) for n=0..39.

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, Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 253-287.

D. J. Broadhurst, Conjectured enumeration of Vassiliev invariants, arXiv:q-alg/9709031, 1997 [different conjectured values].

Jan Kneissler, The number of primitive Vassiliev invariants of degree up to 12, arXiv:q-alg/9706022, 1997.

Index entries for sequences related to knots

Formula

G.f.: Product_{ m >= 1 } (1-y^m)^(-A014605(m)). - Andrey Zabolotskiy, Sep 15 2017

Mathematica

terms = 40; QP = QPochhammer; A014605 = Join[{1, 0, 0, 0}, CoefficientList[ QP[q^4]/QP[q] + O[q]^terms, q]] // Accumulate;
gf = Product[(1 - y^m)^(-A014605[[m+1]]), {m, 1, terms}] + O[y]^terms;
CoefficientList[gf, y] (* Jean-François Alcover, Jul 21 2018 *)

Crossrefs

Cf. A014605 (conjectured to agree with A007478), A014596 (first differences, conjectured to agree with A007293). This sequences is conjectured to agree with A007473. All these (equivalent) conjectures are probably wrong since Jan Kneissler states that A007478(13) >= 78 (see A007478), while A014605(13)=77.

Sequence in context: A378672 A244742 A007473 * A079959 A282583 A028495

Adjacent sequences: A014592 A014593 A014594 * A014596 A014597 A014598

Keyword

nonn

Author

David Broadhurst

Extensions

More terms from Joerg Arndt, Sep 19 2017

Status

approved