A307597 - OEIS

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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

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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].