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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access August 20, 2016

A Combinatorial Proof of a Result on Generalized Lucas Polynomials

Alexandre Laugier and Manjil P. Saikia
From the journal Demonstratio Mathematica


We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.


[1] T. Amdeberhan, X. Chen, V. H. Moll, B. E. Sagan, Generalized Fibonacci polynomials and Fibonomial coefficients, Ann. Comb. 18(4) (2014), 541-562.10.1007/s00026-014-0242-9Search in Google Scholar

[2] S. Ekhad, The Sagan-Savage Lucas-Catalan polynomials have positive coefficients, preprint in Google Scholar

[3] B. E. Sagan, C. D. Savage, Combinatorial interpretations of binomial coefficient analogues related to Lucas sequences, Integers, A52, 10 (2010), 697-703.Search in Google Scholar

Received: 2014-3-26
Published Online: 2016-8-20
Published in Print: 2016-9-1

© by Manjil P. Saikia

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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