MathDB

Let

n

be a positive integer. Find the number of sequences

a_1,a_2,...,a_k

of different numbers from

\{ 1,2,3,...,n\}

with the following property: for every number

a

of the sequence (except the first one) there exists a previous number

b

such that their difference is

1

(so

a-b= \pm 1

)

Problem Statement