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