The Tilings of a (2× n)-Board and Some New Combinatorial Identities
نویسنده
چکیده
We know that the Fibonacci numbers count the tilings of a (1×n)-board by squares and dominoes, or equivalently, the number of tilings of a (2×n)-board by dominoes. We use the tilings of a (2×n)-board by colored unit squares and dominoes to obtain some new combinatorial identities. They are generalization of some known combinatorial identities and in the special case give us the Fibonacci identities.
منابع مشابه
Tiling a (2 × n)-Board with Squares and Dominoes
The Fibonacci numbers and the Pell numbers can be interpreted as the number of tilings of a (1 × n)-board by colored squares and dominoes. We explore the tilings of (2 × n)-boards by colored squares and dominoes. We develop a recurrence relation and prove several combinatorial identities in the style of recent work by Benjamin and Quinn. We also give a bijection between these (2 × n)-tilings an...
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