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