MathDB

Let

n

be a fixed positive integer. How many ways are there to write

n

as a sum of positive integers,

n = a_1 + a_2 + \cdots a_k

with

k

an arbitrary positive integer and

a_1 \le a_2 \le \cdots \le a_k \le a_1 + 1

? For example, with

n = 4

, there are four ways:

4

2 + 2

1 + 1 + 2

1 + 1 + 1 + 1

Problem Statement