A q-Analogue of the Bi-Periodic Fibonacci Sequence

  • José L. Ramı́rez, Sergio Arboleda
  • Published 2016

Abstract

The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation tn = atn−1 + tn−2 if n is even, and tn = btn−1 + tn−2 if n is odd, with initial values t0 = 0 and t1 = 1, where a and b are positive integers. This sequence is called the bi-periodic Fibonacci sequence. In the present article, we introduce a q-analog of the bi-periodic Fibonacci sequence, and prove several identities involving this sequence. We also give a combinatorial interpretation of this q-analog bi-periodic Fibonacci sequence in terms of weighted colored tilings.

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Cite this paper

@inproceedings{Ramrez2016AQO, title={A q-Analogue of the Bi-Periodic Fibonacci Sequence}, author={Jos{\'e} L. Ramı́rez and Sergio Arboleda}, year={2016} }