Numbers that are not the sum of 3 generalized 13-gonal numbers.
4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 22, 25, 28, 29, 34, 35, 40, 43, 48, 52, 53, 55, 58, 60, 61, 66, 69, 78, 79, 87, 88, 91, 92, 97, 105, 110, 113, 118, 121, 122, 123, 124, 131, 144, 145, 148, 149, 154, 158, 163, 165, 166, 167, 175, 190, 193, 199, 211, 218, 219
1
It appears that 10795 is the last number not representable as the sum of 3 generalized 13-gonal numbers.
T. D. Noe, Plot of 196 terms
T. D. Noe, Table of 196 terms
Eric W. Weisstein, MathWorld: Polygonal Number
(Mma) f = 13; 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,fini
T. D. Noe, Dec 28 2015