Let m(k) be the index of the largest triangular number <= k; then a(n) is the smallest number k that can be written as the sum of three triangular numbers if the largest is the (m(k)-n)-th triangular number, but no larger.

A331753

Let m(k) be the index of the largest triangular number <= k; then a(n) is the smallest number k that can be written as the sum of three triangular numbers if the largest is the (m(k)-n)-th triangular number, but no larger.