Where records occur in the number of partitions of n into 4 squares of integers.
0, 1, 2, 3, 4, 10, 12, 18, 27, 28, 42, 52, 66, 82, 90, 130, 138, 150, 162, 198, 210, 234, 258, 294, 306, 330, 378, 450, 522, 570, 630, 810, 882, 990, 1050, 1170, 1350, 1386, 1530, 1638, 1650, 1890, 2250, 2310, 2610, 2730, 2970, 3150, 3330, 3510, 3570, 3990
1
Where records occur 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}]; Table[Position[t, b, 1, 1][[1, 1]] - 1, {b, tMax}]
nonn
T. D. Noe, May 16 2016