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 A349523 #9 Nov 20 2021 21:35:32
%S A349523 1,2,3,5,6,9,11,13,14,18,20,23,24,29,31,35,38,41,42,48,50,55,58,62,63,
%T A349523 70,72,78,81,86,90,94,95,103,105,112,115,121,125,130,131,140,142,150,
%U A349523 153,160,164,170,175,180,181,191,193,202,205,213,217,224,229,235,236,247,249
%N A349523 a(n) = Sum_{k=1..n} A339399(k).
%C A349523 Partial sums of A339399.
%H A349523 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A349523 a(n) = Sum_{i=1..n} ((1+(-1)^i)*(1+floor(sqrt(2*i-1-(-1)^i)))/2-((2*i+1-(-1)^i)/2-2 *Sum_{k=1..floor(sqrt(2*i-2-(-1)^i)-1)} floor((k+1)/2))*(-1)^i/2).
%F A349523 a(n) = Sum_{k=1..n} A339443(A103889(k)).
%t A349523 Table[Sum[((1 + (-1)^k) (1 + Floor[Sqrt[2 k - 1 - (-1)^k]])/2 - ((2 k + 1 - (-1)^k)/2 - 2 Sum[Floor[(i + 1)/2], {i, -1 + Floor[Sqrt[2 k - 2 - (-1)^k]]}]) (-1)^k/2), {k, n}], {n, 100}]
%Y A349523 Cf. A103889, A339399, A339443.
%K A349523 nonn
%O A349523 1,2
%A A349523 _Wesley Ivan Hurt_, Nov 20 2021