Summing a family of generalized Pell numbers

Helmut Prodinger

Published: 2020-12-14

Vol. 35 No. 1 (2021)

Summing a family of generalized Pell numbers

Helmut Prodinger

Abstract

A new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power P_n^l is expressed as a linear combination of P_mn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R=2^r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.

Keywords:

Pell numbers , Binet formula , generating functions

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Prodinger, H. (2020). Summing a family of generalized Pell numbers. Annales Mathematicae Silesianae, 35(1), 105–112. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13477

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Vol. 35 No. 1 (2021)
Published: 2021-02-10

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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