MathDB

Given an integer

n > 1

, consider words composed of

n

letters

A

and

n

letters

B

. A word

X_1...X_{2n}

is said to belong to set

R(n)

(respectively,

S(n)

) if no initial segment (respectively, exactly one initial segment)

X_1...X_k

with

1 \le k < 2n

consists of equally many letters

A

and

B

. If

r(n)

and

s(n)

denote the cardinalities of

R(n)

and

S(n)

respectively, compute

s(n)/r(n)

Problem Statement