Numbers that are not the sum of 3 generalized 16-gonal numbers.
4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 22, 23, 24, 25, 28, 31, 34, 35, 36, 37, 38, 43, 44, 49, 50, 51, 52, 55, 60, 63, 64, 65, 67, 68, 70, 73, 75, 76, 78, 79, 84, 87, 92, 99, 100, 108, 109, 111, 112, 115, 116, 118, 119, 123, 124, 131, 132, 140, 143, 148, 151
1
This appears to be an infinite series.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, MathWorld: Polygonal Number
(Mma) f = 16; nn = 100; t = Table[k ((f - 2) k - (f - 4))/2, {k, -nn, nn}]; t2 = Select[Union[Flatten[Table[a + b + c, {a, t}, {b, t}, {c, t}]]], # <= t[[-1]] &]; Complement[Range[t[[-1]]], t2]
nonn
T. D. Noe, Dec 28 2015