Numbers that are not the sum of 3 generalized 19-gonal numbers.

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 37, 40, 41, 42, 43, 44, 45, 46, 47, 52, 53, 58, 59, 60, 61, 62, 63, 64, 67, 72, 75, 76, 77, 78, 79, 80, 82, 83, 85, 88, 90, 91, 93, 94, 95, 96, 97, 102, 105, 110, 111, 112

1

It appears that 122818 is the last number not representable as the sum of 3 generalized 19-gonal numbers.

T. D. Noe, Plot of 999 terms

T. D. Noe, Table of 999 terms

Eric W. Weisstein, MathWorld: Polygonal Number

(Mma) f = 19; nn = 200; 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,fini

T. D. Noe, Dec 28 2015