Journal of Integer Sequences, Vol. 12 (2009), Article 09.1.6

On the Expansion of Fibonacci and Lucas Polynomials

Helmut Prodinger
Department of Mathematics
University of Stellenbosch
7602 Stellenbosch
South Africa


Recently, Belbachir and Bencherif have expanded Fibonacci and Lucas polynomials using bases of Fibonacci- and Lucas-like polynomials. Here, we provide simplified proofs for the expansion formulae that in essence a computer can do. Furthermore, for 2 of the 5 instances, we find q-analogues.

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(Concerned with sequences A007318 A029653 and A112468.)

Received October 6 2008; revised version received December 15 2008. Published in Journal of Integer Sequences, December 17 2008.

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