A014605 Partial sums of A001935; at one time this was conjectured to agree with A007478.

1, 1, 1, 1, 2, 3, 5, 8, 12, 18, 27, 39, 55, 77, 106, 144, 194, 258, 340, 445, 577, 743, 951, 1209, 1529, 1924, 2408, 3000, 3722, 4598, 5658, 6938, 8477, 10323, 12533, 15169, 18307, 22035, 26451, 31673, 37836, 45092, 53620, 63626, 75342, 89038, 105024, 123648

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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

D. Bar-Natan, Bibliography of Vassiliev Invariants

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

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

a(n) = a(n-1) + A001935(n-4), n>3. - R. J. Mathar, Mar 06 2016

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(`if`(
      irem(d, 4)=0, 0, d), d=numtheory[divisors](j)), j=1..n)/n)
    end:
a:= proc(n) option remember; `if`(n<4, 1, a(n-1)+b(n-4)) end:
seq(a(n), n=0..60);  # Alois P. Heinz, Jul 21 2018

Mathematica

QP = QPochhammer; Join[{1, 0, 0, 0}, CoefficientList[QP[q^4]/QP[q]+O[q]^50, q]] // Accumulate (* Jean-François Alcover, Jul 21 2018 *)

Crossrefs

Sequence in context: A328170 A078408 A007478 * A365828 A232477 A232478

Adjacent sequences: A014602 A014603 A014604 * A014606 A014607 A014608

Keyword

nonn

Author

David Broadhurst

Status

approved