Journal of Integer Sequences, Vol. 25 (2022), Article 22.3.5

Scaled Fibonacci- and Lucas-Producing Rational Polynomials


Brian Hopkins
Department of Mathematics and Statistics
Saint Peter's University
Jersey City, NJ 07306
USA

Aram Tangboonduangjit
Mahidol University International College
Mahidol University
Salaya, Nakhon Pathom 73170
Thailand

Abstract:

We study families of interpolating rational polynomials that produce scaled Fibonacci or Lucas numbers on certain integer values. We use the expansions of these families in binomial polynomials and other formats to establish several identities involving harmonic numbers, binomial coefficients, and various recursively defined sequences.

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(Concerned with sequences A000032 A000045 A001008 A002805 A005013 A005247 A007318 A052568 A078700.)

Received February 14 2022; revised versions received March 13 2022; March 16 2022. Published in Journal of Integer Sequences, March 24 2022.

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