MathDB

For positive integers

k

and

n

, express the number of permutation

P=x_1x_2...x_{2n}

consisting of

A

and

B

that satisfies all three of the following conditions, using

k

and

n

(i)

A, B

appear exactly

n

times respectively in

P

(ii)

For each

1\le i\le n

, if we denote the number of

A

x_1,x_2,...,x_i

a_i

,

then

\mid 2a_i -i\mid \le 1

(iii)

AB

appears exactly

k

times in

P

. (For example,

AB

appears 3 times in

ABBABAAB

)

Problem Statement