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 A165453 #26 Jun 19 2024 15:07:05
%S A165453 0,1,2,4,6,8,10,13,16,19,22,25,28,32,36,40,44,48,52,56,60,65,70,75,80,
%T A165453 85,90,95,100,105,110,116,122,128,134,140,146,152,158,164,170,176,182,
%U A165453 189,196,203,210,217,224,231,238,245,252,259,266,273,280,288,296,304
%N A165453 Linear interpolation of the sequence that maps an entry of A002378 to the corresponding entry of A006331.
%F A165453 a(0)=0, a(n) = max(min(a(n-1)+x, n+a(n-x))), where the maximum is taken over all values for x from 1 to n.
%F A165453 a(n) = Sum_{k=1..n} floor(sqrt(k)+1/2). - _Wesley Ivan Hurt_, Dec 01 2020
%F A165453 a(n) = (1/3)*t*(3*n + 1 - t^2), where t = floor(sqrt(n)+1/2). - _Ridouane Oudra_, Feb 22 2021
%t A165453 f[n_]:=Round[Sqrt[n]]; a=0;lst={};Do[AppendTo[lst,a+=f[n]],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 13 2009 *)
%t A165453 Table[Sum[Floor[Sqrt[n + 1 - k] + 1/2], {k, n + 1}], {n, 0, 100}] (* _Wesley Ivan Hurt_, Dec 01 2020 *)
%o A165453 (Python)
%o A165453 from math import isqrt
%o A165453 def A165453(n): return (k:=(m:=isqrt(n))+(n-m*(m+1)>=1))*(3*n+1-k**2)//3 # _Chai Wah Wu_, Jun 19 2024
%Y A165453 Cf. A002378, A006331.
%Y A165453 Partial sums of A000194.
%K A165453 easy,nonn
%O A165453 0,3
%A A165453 Friedrich Regen (friedrich.regen(AT)tu-ilmenau.de), Sep 20 2009