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A Generalized Binet Formula That Counts the Tilings of a (2 x n)-board

In this paper, we answer an open problem raised by Katz and Stenson. They considered the tilings of a (2 ⇥ n)-board using a colors of squares and b colors of dominoes. The number of such tilings, denoted by Ka,b n , is a generalization of the Fibonacci numbers. Obtaining a Binet-style formula for these numbers is such problem. We obtain a generalized Binet formula for Ka,b n .