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A014595 Conjectured dimensions of spaces of weight systems of chord diagrams. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
First 13 terms agree with A007473, next terms obtained from A014605.
LINKS
D. Bar-Natan, On the Vassiliev Knot Invariants, Topology 34 (1995) 423-472.
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.
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: A217382 A244742 A007473 * A079959 A282583 A028495
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Joerg Arndt, Sep 19 2017
STATUS
approved

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Last modified March 29 02:12 EDT 2024. Contains 371264 sequences. (Running on oeis4.)