MathDB

How many permutations

a_1, a_2, \ldots, a_n

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

are sorted into increasing order by at most three repetitions of the following operation: Move from left to right and interchange

a_i

and

a_{i+1}

whenever

a_i > a_{i+1}

for

i

running from

1

up to

n - 1 \ ?

Problem Statement