MathDB

Find the number of permutations

( a_1, a_2, . \ . \ , a_{2016})

of the first

2016

positive integers satisfying the following two conditions:
1.

a_{i+1} - a_i \leq 1

for all

i = 1, 2, . \ . \ . , 2015

, and 2. There are exactly two indices

i < j

with

1 \leq i < j \leq 2016

such that

a_i = i

and

a_j = j

Problem Statement