Pseudocode for less naive 3-partition finder:

integer less_naive_3_partition_finder
	input: an positive integer n
	output: number of triples (a, b, c) such that a, b, and c are
			positive integers and a + b + c = n

	total = 0
	for a in 1...n
		for b in 1...(n-a)
			c = n - (a + b)
			if c > 0
				total += 1
	return total