Journal of Integer Sequences, Vol. 20 (2017), Article 17.5.4

The Tilings of a (2 × n)-Board and Some New Combinatorial Identities

Reza Kahkeshani
Department of Pure Mathematics
Faculty of Mathematical Sciences
University of Kashan


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.

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(Concerned with sequences A000045 A000129 A030186 A253265.)

Received May 17 2016; revised versions received October 14 2016; October 19 2016; March 28 2017. Published in Journal of Integer Sequences, April 8 2017.

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