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 A065611 #20 Mar 24 2020 08:40:51
%S A065611 1,35721,9,64,150700176,1521,1718434116,3844,1849,900,2209,474721,529,
%T A065611 116964,400,419845682025,618399795456,3600,187489,1734149230641,10816,
%U A065611 1681,5560164,2025,961,1444,961,784,41209,21926752125201
%N A065611 Let k be the least integer such that n^2 + Sum_{m=1..k} m^2 is a perfect square, then a(n) is the resulting square.
%C A065611 I.e., n^2 + {1 + 4 + 9 + 16 + ... + m^2} = a(n) = A065612(n)^2 = A065311(n). a(n) is the smallest square obtained as n^2 + x*(x+1)*(2x+1)/6 where x = A065610(n).
%H A065611 Harry J. Smith, <a href="/A065611/b065611.txt">Table of n, a(n) for n = 0..500</a>
%e A065611 n = 3: a(3) = 64 because n^2 + 1 + 4 + 9 + 16 + 25 = 9 + (1 + 4 + 9 + 16 + 25) = 64 = 8^2;
%e A065611 n = 4: a(4) = 150700176 because n^2 + (1 + 4 + ... + 767^2) = 150700176 = 12276^2, where 767 is the length of the shortest such consecutive-square sequence which provides(when summed) a new square, namely 12276^2. Often the least solution is rather large. E.g., a(93) = 23850559947150225 which means that 93^2 + A000330(415151) = 8649 + [a long square sum] = 154436265^2 = 23850559947150225.
%t A065611 Do[s = n^2; k = 1; While[s = s + k^2; !IntegerQ[ Sqrt[s]], k++ ]; Print[s], {n, 0, 30} ]
%o A065611 (PARI) { for (n = 0, 500, s=n^2 + 1; k=1; while (!issquare(s), k++; s+=k^2); write("b065611.txt", n, " ", s) ) } \\ _Harry J. Smith_, Oct 23 2009
%o A065611 (PARI) a(n) = my(s=n^2+1, k=1); while (!issquare(s), k++; s+=k^2); s; \\ _Michel Marcus_, Mar 24 2020
%Y A065611 Cf. A000330, A065610, A065612.
%K A065611 nonn
%O A065611 0,2
%A A065611 _Labos Elemer_, Nov 07 2001
%E A065611 Edited by _Jon E. Schoenfield_, Jun 14 2018
%E A065611 Name clarified by _Michel Marcus_, Mar 24 2020