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 A001182 #26 Jul 18 2024 21:02:35
%S A001182 0,1,4,8,15,22,30,41,54,69,83,98,119,139,162,183,208,234,263,294,322,
%T A001182 357,390,424,465,504,545,585,628,675,719,770,819,872,928,977,1036,
%U A001182 1090,1155,1216,1274,1339,1404,1475,1545,1610,1683,1755,1832,1911,1992,2072
%N A001182 Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0.
%H A001182 Michael De Vlieger, <a href="/A001182/b001182.txt">Table of n, a(n) for n = 1..10000</a>
%F A001182 a(n) = Sum_{k=1..n-1} floor(sqrt(n^2-k^2)). - Horst Kraemer (horst.kraemer(AT)epost.de) Apr 07 2004
%F A001182 a(n) = A261849(2*n)/4 = (A281795(n)-A242118(n))/4. - _Andrey Zabolotskiy_, Jan 30 2017
%F A001182 a(n) = [x^(n^2)] (theta_3(x) - 1)^2/(4*(1 - x)), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Apr 17 2018
%t A001182 Table[Sum[Floor@ Sqrt[n^2 - k^2], {k, n - 1}], {n, 52}] (* _Michael De Vlieger_, Jan 30 2017 *)
%o A001182 (Python)
%o A001182 from math import isqrt
%o A001182 def A001182(n): return sum(isqrt(k*((n<<1)-k)) for k in range(1,n)) # _Chai Wah Wu_, Jul 18 2024
%Y A001182 Cf. A261849, A242118, A281795.
%K A001182 nonn
%O A001182 1,3
%A A001182 Tihamer von Ghyczy (ghyczy(AT)esinet.net)
%E A001182 More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000