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 A162397 #22 Nov 23 2023 08:00:59
%S A162397 1,-2,0,4,-5,0,7,-8,0,10,-11,0,13,-14,0,16,-17,0,19,-20,0,22,-23,0,25,
%T A162397 -26,0,28,-29,0,31,-32,0,34,-35,0,37,-38,0,40,-41,0,43,-44,0,46,-47,0,
%U A162397 49,-50,0,52,-53,0,55,-56,0,58,-59,0,61,-62,0,64,-65,0
%N A162397 a(n) = n * Kronecker(-3, n).
%C A162397 In Gil and Robins 2003 on page 33 the g.f. is denoted by f_{4, 2}(x). - _Michael Somos_, Sep 04 2015
%D A162397 George E. Andrews and Bruce C. Berndt, Ramanujan's lost notebook, Part I, Springer, New York, 2005, MR2135178 (2005m:11001) See p. 319, Equation (14.3.6).
%H A162397 Juan B. Gil and Sinai Robins, <a href="http://arxiv.org/abs/math/0309244">Hecke operators on rational functions</a>, arXiv:math/0309244 [math.NT], 2003.
%F A162397 Euler transform of length 3 sequence [ -2, -1, 2].
%F A162397 a(n) is completely multiplicative with a(3^e) = 0^e, a(p^e) = p^e if p == 1 (mod 3), a(p^e) = (-p)^e if p == 2 (mod 3).
%F A162397 G.f.: (x - x^3) / (1 + x + x^2)^2.
%F A162397 a(3*n) = 0. a(n) = a(-n). abs(a(n)) = A091684(n). a(n) = n * A102283(n). a(3*n + 1) = A016777(n). a(3*n + 2) = - A016789(n). - _Michael Somos_, Mar 14 2012
%F A162397 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2/3. - _Amiram Eldar_, Nov 23 2023
%e A162397 G.f. = x - 2*x^2 + 4*x^4 - 5*x^5 + 7*x^7 - 8*x^8 + 10*x^10 - 11*x^11 + ...
%t A162397 Table[n*KroneckerSymbol[-3,n],{n,80}] (* _Harvey P. Dale_, Mar 14 2015 *)
%o A162397 (PARI) {a(n) = n * kronecker(-3, n)};
%Y A162397 Cf. A016777, A016789, A091684, A102283.
%K A162397 sign,easy,mult
%O A162397 1,2
%A A162397 _Michael Somos_, Jul 02 2009