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A350143 a(n) = Sum_{k=1..n} floor(n/(2*k-1))^2.

%I A350143 #22 Feb 01 2024 22:52:43
%S A350143 1,4,10,17,27,41,55,70,93,115,137,167,193,223,267,298,332,381,419,465,
%T A350143 525,571,617,679,738,792,868,930,988,1080,1142,1205,1297,1367,1459,
%U A350143 1560,1634,1712,1820,1914,1996,2120,2206,2300,2450,2544,2638,2764,2875,2996,3136,3246
%N A350143 a(n) = Sum_{k=1..n} floor(n/(2*k-1))^2.
%H A350143 Winston de Greef, <a href="/A350143/b350143.txt">Table of n, a(n) for n = 1..10000</a>
%F A350143 a(n) = Sum_{k=1..n} Sum_{d|k, k/d odd} 2*d - 1 = Sum_{k=1..n} 2 * A002131(k) - A001227(k) = 2 * A350146(n) - A060831(n).
%F A350143 G.f.: (1/(1 - x)) * Sum_{k>=1} (2*k - 1) * x^k/(1 - x^(2*k)).
%t A350143 a[n_] := Sum[Floor[n/(2*k - 1)]^2, {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Dec 17 2021 *)
%o A350143 (PARI) a(n) = sum(k=1, n, (n\(2*k-1))^2);
%o A350143 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, k/d%2*(2*d-1)));
%o A350143 (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 A350143 Column 2 of A350122.
%Y A350143 Cf. A001227, A002131, A060831, A350146.
%K A350143 nonn
%O A350143 1,2
%A A350143 _Seiichi Manyama_, Dec 16 2021