Records in the number of partitions of n into 4 squares of integers.
1, 2, 4, 8, 18, 20, 24, 28, 32, 48, 56, 68, 72, 92, 116, 136, 144, 152, 172, 192, 240, 244, 248, 256, 308, 336, 416, 480, 500, 576, 696, 836, 876, 936, 1112, 1240, 1352, 1392, 1528, 1576, 1656, 2112, 2248, 2400, 2584, 2784, 3072, 3224, 3256, 3552, 3648, 3936
1
Records in S000883.
T. D. Noe, Plot of 98 terms
T. D. Noe, Table of 98 terms
Wikipedia, Lagrange's four-square theorem
(Mma) lim = 50; nn = (lim + 1)^2; t = Table[0, {nn}]; Do[n = x^2 + y^2 + z^2 + w^2; If[n < nn, t[[n + 1]]++], {x, -lim, lim}, {y, -Abs[x], Abs[x]}, {z, -Abs[y], Abs[y]}, {w, -Abs[z], Abs[z]}]; mx = -1; tMax = {}; Do[If[k > mx, mx = k; AppendTo[tMax, k]], {k, t}]; tMax
nonn
T. D. Noe, May 16 2016