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 A374532 #17 Jul 19 2024 14:31:15 %S A374532 0,4,12,24,40,68,96,132,180,224,284,340,408,492,564,656,740,848,960, %T A374532 1060,1184,1304,1444,1576,1704,1868,2024,2196,2356,2520,2716,2892, %U A374532 3104,3292,3504,3720,3916,4160,4384,4628,4872,5108,5372,5640,5916,6188,6456,6764,7036 %N A374532 Number of complete unit squares that fit inside a circle of radius sqrt(n^2+1) centered at the origin of a square lattice. %H A374532 Thomas Otten, <a href="/A374532/a374532.png">Illustration of initial terms</a>. %F A374532 a(n) = 4*A237526(n^2 + 1). %o A374532 (PARI) a(n) = my(s=n^2+1); 4*sum(k=1, sqrtint(s), sqrtint(s-k^2)) \\ _Andrew Howroyd_, Jul 11 2024 %o A374532 (Python) %o A374532 def A374532(n): return sum(isqrt(k*((n<<1)-k)+1) for k in range(n))<<2 # _Chai Wah Wu_, Jul 18 2024 %Y A374532 Cf. A119677 (case for radius of n), A237526. %Y A374532 Cf. A046092, A000328 (quadrant width 1 cell). %K A374532 nonn %O A374532 0,2 %A A374532 _Thomas Otten_, Jul 10 2024