The Tilings of a (2 × n)-Board and Some New Combinatorial Identities
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
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.
Full version: pdf,
(Concerned with sequences
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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