cp's OEIS Frontend

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

%I A014605 #26 Sep 03 2025 13:10:44
%S A014605 1,1,1,1,2,3,5,8,12,18,27,39,55,77,106,144,194,258,340,445,577,743,
%T A014605 951,1209,1529,1924,2408,3000,3722,4598,5658,6938,8477,10323,12533,
%U A014605 15169,18307,22035,26451,31673,37836,45092,53620,63626,75342,89038,105024,123648
%N A014605 Partial sums of A001935; at one time this was conjectured to agree with A007478.
%H A014605 Alois P. Heinz, <a href="/A014605/b014605.txt">Table of n, a(n) for n = 0..10000</a>
%H A014605 Bar-Natan, Dror, <a href="http://www.math.toronto.edu/drorbn/LOP.html#OnVassiliev">On the Vassiliev Knot Invariants</a>, Topology 34 (1995) 423-472.
%H A014605 D. Bar-Natan, <a href="http://www.math.toronto.edu/drorbn/LOP.html">Bibliography of Vassiliev Invariants</a>
%H A014605 Joan S. Birman, <a href="https://doi.org/10.1090/S0273-0979-1993-00389-6">New points of view in knot theory</a>, Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 253-287.
%H A014605 Jan Kneissler, <a href="http://arxiv.org/abs/q-alg/9706022">The number of primitive Vassiliev invariants of degree up to 12</a>, arXiv:q-alg/9706022, 1997.
%H A014605 <a href="/index/K#knots">Index entries for sequences related to knots</a>
%F A014605 a(n) = a(n-1) + A001935(n-4), n>3. - _R. J. Mathar_, Mar 06 2016
%p A014605 b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(`if`(
%p A014605       irem(d, 4)=0, 0, d), d=numtheory[divisors](j)), j=1..n)/n)
%p A014605     end:
%p A014605 a:= proc(n) option remember; `if`(n<4, 1, a(n-1)+b(n-4)) end:
%p A014605 seq(a(n), n=0..60);  # _Alois P. Heinz_, Jul 21 2018
%t A014605 QP = QPochhammer; Join[{1, 0, 0, 0}, CoefficientList[QP[q^4]/QP[q]+O[q]^50, q]] // Accumulate (* _Jean-François Alcover_, Jul 21 2018 *)
%K A014605 nonn,changed
%O A014605 0,5
%A A014605 _David Broadhurst_