MathDB

Let

S(n)

denote the number of sequences of length

n

formed by the three letters

A,B,C

with the restriction that the

C

's (if any) all occur in a single block immediately following the first

B

(if any). For example

ABCCAA

AAABAA

, and

ABCCCC

are counted in, but

ACACCB

and

CAAAAA

are not. Derive a simple formula for

S(n)

and use it to calculate

S(10)

Problem Statement