2

Part of 2004 Czech and Slovak Olympiad III A

Problems(1)

n-letter words containing two letters

Source: Czech and Slovak third round,2004,p2

Consider all words containing only letters

A

B

. For any positive integer

n

p(n)

denotes the number of all

n

-letter words without four consecutive

A

's or three consecutive

B

's. Find the value of the expression

\frac{p(2004)-p(2002)-p(1999)}{p(2001)+p(2000)}.

algebrasystem of equationscombinatorics proposedcombinatorics