A307598 Number of partitions of n into 3 distinct positive triangular numbers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 1, 0, 3, 0, 2, 1, 1, 1, 1, 2, 1, 2, 1, 0, 3, 1, 0, 4, 1, 2, 1, 1, 1, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 1, 3, 2, 2, 2, 2, 1, 3, 2, 0, 4, 1, 1, 5, 1, 3, 2, 2, 3, 2, 2, 1, 4, 1, 2, 4, 2, 2, 3, 2, 1, 3, 2, 4, 3, 3, 2, 2, 3, 1, 6

Offset

0,20

Comments

The greedy inverse starts 0, 10, 19, 37, 52, 82, 109, 136, 241, 226, 217, 247, 364, 427, 457, 541, 532, 577, 637, 961, 721, 787, 1066, 1102, 1381, 1267, 1564, 1192, 1396, 1816, 1501, 1612, 1927, 1942, 2242, 1792, 2842, 2587, 2557, 2422, ... - R. J. Mathar, Apr 28 2020

Links

Table of n, a(n) for n=0..109.

Formula

a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^(k*(k+1)/2)).

Example

a(19) = 2 because we have [15, 3, 1] and [10, 6, 3].

Crossrefs

Cf. A000217, A002244, A008443, A024940, A025442, A053604, A063993, A224326, A307597.

Sequence in context: A069859 A179317 A330657 * A324967 A320332 A358007

Adjacent sequences: A307595 A307596 A307597 * A307599 A307600 A307601

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 17 2019

Status

approved