This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364235 #13 Jul 29 2023 10:35:51 %S A364235 0,1,0,-2,1,3,0,-3,0,3,1,-6,0,8,3,-10,1,9,0,-13,0,9,1,-9,5,14,0,-16,1, %T A364235 9,0,-19,3,15,8,-18,0,20,0,-25,1,24,0,-25,9,21,1,-30,0,16,3,-28,1,27, %U A364235 16,-24,0,27,1,-39,0,32,0,-42,14,27,0,-37,3,24,1,-27,0,38,15,-40,8,42,0,-69 %N A364235 Expansion of Sum_{k>=0} x^(3*k+2) / (1 + x^(3*k+2))^2. %H A364235 Seiichi Manyama, <a href="/A364235/b364235.txt">Table of n, a(n) for n = 1..10000</a> %F A364235 a(n) = Sum_{d|n, n/d==2 (mod 3)} (-1)^(d+1) * d. %t A364235 nmax = 80; CoefficientList[Series[Sum[x^(3 k + 2)/(1 + x^(3 k + 2))^2, {k, 0, nmax}], {x, 0, nmax}], x] // Rest %t A364235 Table[DivisorSum[n, (-1)^(# + 1) # &, MemberQ[{2}, Mod[n/#, 3]] &], {n, 1, 80}] %Y A364235 Cf. A002129, A186690, A326400, A364015, A364205, A364232. %K A364235 sign %O A364235 1,4 %A A364235 _Ilya Gutkovskiy_, Jul 14 2023