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A118282 Conjectured largest number that is not the sum of three generalized n-gonal numbers, or -1 if there is no largest number. 3
0, -1, 0, 0, 307, -1, 2027, 5200, 18180, -1, 10795, -1, 87740, -1, 75150, 212048, 122818, -1, 146970, 199153, 585513 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=3..23.


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

Sequence in context: A035843 A128477 A028680 * A220475 A282594 A050201

Adjacent sequences:  A118279 A118280 A118281 * A118283 A118284 A118285




T. D. Noe, Apr 21 2006



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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)