MATHCOUNTS Chapter 2026 Team Round (Problem 9)

A sequence is said to be non-decreasing when each term is greater than or equal to the term before it. For example,

4,4,4,5,6

is non-decreasing, but

4,4,4,3,5,6

is not because

3

is less than

4

, and

3

comes after

4

in the sequence. How many non-decreasing sequences of positive integers with length

2026

terms start with

1

and end with

3