A118282 Conjectured largest number that is not the sum of three generalized n-gonal numbers, or -1 if there is no largest number.

0, -1, 0, 0, 307, -1, 2027, 5200, 18180, -1, 10795, -1, 87740, -1, 75150, 212048, 122818, -1, 146970, 199153, 585513

Offset: 3

Author

T. D. Noe, Apr 21 2006

Keywords

• sign

Comments

Extensive calculations show that if a(n)>=0, then every number greater than a(n) can be represented as the sum of three generalized n-gonal numbers. a(n)=0 for n=3 and 6 because generalized triangular and generalized hexagonal numbers are the same a triangular numbers and every number can be written as the sum of three triangular numbers. When n is a multiple of 4, there is an infinite set of numbers not representable. For n=14, there appears to be a sparse, but infinite, set of numbers not representable. See A118283 for the number of numbers not representable.

Crossrefs

Cf. A001318 (generalized pentagonal numbers), A085787 (generalized heptagonal numbers), A001082 (generalized octagonal numbers), A118277 (generalized 9-gonal numbers), A118278-A118285.