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 A212649 #28 Oct 27 2024 03:25:20
%S A212649 1,3,8,13,21,30,41,53,67,82,99,118,138,159,183,207,234,262,291,322,
%T A212649 355,389,425,462,501,542,584,628,673,720,768,818,870,923,977,1034,
%U A212649 1091,1151,1212,1274,1338,1404,1471,1540,1610,1682,1756,1831,1908,1986,2066
%N A212649 a(n) = floor(Sum_{k=0..n-1} sqrt(n^2 - k^2)).
%C A212649 Limit_{n->oo} a(n)/n^2 = Pi/4 = 0.78539816...
%F A212649 a(n) = floor(Sum_{k=0..n-1} sqrt(A094728(n,k))).
%e A212649 A094728(4) is (16, 15, 12, 7). Hence, a(4) = floor(sqrt(16) + sqrt(15) + sqrt(12) + sqrt(7)) = floor(13.9828...) = 13.
%t A212649 Table[Floor[Sum[Sqrt[n^2 - k^2], {k, 0, n - 1}]], {n, 60}] (* _T. D. Noe_, Mar 19 2013 *)
%Y A212649 Cf. A003881, A094728.
%K A212649 nonn,easy
%O A212649 1,2
%A A212649 _Philippe Deléham_, Mar 07 2013
%E A212649 a(16)-a(50) from _Giovanni Resta_, Mar 19 2013