cp's OEIS Frontend

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.

A345035 a(n) = Sum_{k=1..n} (-3)^(floor(n/k) - 1).

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%I A345035 #15 Jun 07 2021 09:10:07
%S A345035 1,-2,11,-28,81,-234,739,-2216,6545,-19594,59139,-177408,531181,
%T A345035 -1593614,4783799,-14351032,43044597,-129133854,387426799,-1162281332,
%U A345035 3486765521,-10460293354,31381119459,-94143358440,282429356977,-847288080362,2541866366171
%N A345035 a(n) = Sum_{k=1..n} (-3)^(floor(n/k) - 1).
%H A345035 Seiichi Manyama, <a href="/A345035/b345035.txt">Table of n, a(n) for n = 1..2000</a>
%F A345035 G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + 3*x^k).
%t A345035 a[n_] := Sum[(-3)^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 30] (* _Amiram Eldar_, Jun 06 2021 *)
%o A345035 (PARI) a(n) = sum(k=1, n, (-3)^(n\k-1));
%o A345035 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1+3*x^k))/(1-x))
%Y A345035 Column k=3 of A345033.
%Y A345035 Cf. A014983, A345029.
%K A345035 sign
%O A345035 1,2
%A A345035 _Seiichi Manyama_, Jun 06 2021