MathDB
n-letter words containing two letters

Source: Czech and Slovak third round,2004,p2

March 3, 2012
algebrasystem of equationscombinatorics proposedcombinatorics

Problem Statement

Consider all words containing only letters AA and BB. For any positive integer nn, p(n)p(n) denotes the number of all nn-letter words without four consecutive AA's or three consecutive BB's. Find the value of the expression p(2004)−p(2002)−p(1999)p(2001)+p(2000).\frac{p(2004)-p(2002)-p(1999)}{p(2001)+p(2000)}.
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