MathDB

There are only two letters in the Mumu tribe alphabet: M and

U

. The word in the Mumu language is any sequence of letters

M

and

U

, in which next to each letter

M

there is a letter

U

(for example,

UUU

and

UMMUM

are words and

MMU

is not). Let

f(m,u)

denote the number of words in the Mumu language which have

m

times the letter

M

and

u

times the letter

U

. Prove that

f (m, u) - f (2u - m + 1, u) = f (m, u - 1) - f (2u - m + 1, u - 1)

for any

u \ge 2,3 \le m \le 2u

Problem Statement