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A350162 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^2.

%I A350162 #30 Jun 02 2023 01:19:50
%S A350162 1,4,8,15,25,33,45,60,73,95,115,131,157,181,205,236,270,297,333,379,
%T A350162 403,443,487,519,578,632,672,720,778,826,886,949,989,1059,1131,1186,
%U A350162 1260,1332,1388,1482,1564,1612,1696,1776,1858,1946,2038,2102,2187,2308,2380,2490
%N A350162 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^2.
%H A350162 Winston de Greef, <a href="/A350162/b350162.txt">Table of n, a(n) for n = 1..10000</a>
%F A350162 a(n) = Sum_{k=1..n} Sum_{d|k} A101455(k/d) * (2*d - 1) = Sum_{k=1..n} 2 * A050469(k) - A002654(k) = 2 * A350166(n) - A014200(n).
%F A350162 G.f.: (1/(1 - x)) * Sum_{k>=1} (2*k - 1) * x^k/(1 + x^(2*k)).
%t A350162 a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^2, {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Dec 18 2021 *)
%o A350162 (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\(2*k-1))^2);
%o A350162 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d)*(2*d-1)));
%o A350162 (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, (2*k-1)*x^k/(1+x^(2*k)))/(1-x))
%Y A350162 Column 2 of A350161.
%Y A350162 Cf. A002654, A014200, A050469, A101455, A344720, A350143, A350166.
%K A350162 nonn
%O A350162 1,2
%A A350162 _Seiichi Manyama_, Dec 18 2021