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A014605 Partial sums of A001935; at one time this was conjectured to agree with A007478. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 21 2018 *)

CROSSREFS

Sequence in context: A136275 A078408 A007478 * A232477 A232478 A232476

Adjacent sequences:  A014602 A014603 A014604 * A014606 A014607 A014608

KEYWORD

nonn

AUTHOR

David Broadhurst

STATUS

approved

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Last modified August 14 21:07 EDT 2018. Contains 313756 sequences. (Running on oeis4.)