A307597 Number of partitions of n into 2 distinct positive triangular numbers.

0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 3, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 3, 0, 1

Offset

0,17

Comments

The greedy inverse (positions of first occurrence of n) starts 0, 4, 16, 81, 471, 2031, 1381, 11781, 6906, 17956, ... - R. J. Mathar, Apr 28 2020

Links

Alois P. Heinz, Table of n, a(n) for n = 0..65536 (first 10000 terms from David A. Corneth)

Formula

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

a(n) = Sum_{k=1..floor((n-1)/2)} c(k) * c(n-k), where c = A010054. - Wesley Ivan Hurt, Jan 06 2024

Example

a(16) = 2 because we have [15, 1] and [10, 6].

Crossrefs

Cf. A000217, A008441, A024940, A025441, A052344, A053603, A260647, A307598.

Cf. A010054.

Sequence in context: A221314 A326642 A087371 * A307056 A112762 A357520

Adjacent sequences: A307594 A307595 A307596 * A307598 A307599 A307600

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Apr 17 2019

Status

approved