Where records occur in the number of partitions of n into 4 squares.
0, 4, 18, 34, 50, 66, 82, 90, 130, 150, 162, 198, 210, 234, 306, 378, 450, 570, 594, 630, 738, 810, 882, 990, 1050, 1170, 1350, 1386, 1530, 1638, 1650, 1890, 2250, 2310, 2610, 2730, 2898, 2970, 3150, 3330, 3510, 3570, 3990, 4050, 4290, 4410, 4914, 4950
1
Where records occur in A002635.
T. D. Noe, Plot of 105 terms
T. D. Noe, Table of 105 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, 0, lim}, {y, 0, x}, {z, 0, y}, {w, 0, 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