Records in the number of partitions of n into 4 squares.
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 16, 18, 23, 28, 34, 38, 41, 46, 47, 57, 59, 63, 73, 81, 90, 92, 101, 103, 109, 136, 149, 154, 170, 178, 179, 196, 209, 212, 230, 232, 252, 260, 270, 303, 304, 323, 332, 336, 348, 385, 392, 402, 495, 500, 556, 558, 664
1
Record values 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}]; tMax
nonn
T. D. Noe, May 16 2016