<abstract xmlns="http://www.w3.org/1999/xhtml">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 <italic>P</italic>𝓁<italic>n</italic> is expressed as a linear combination of <italic>P</italic><italic>mn</italic>. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter <italic>R</italic> = 2<italic>r</italic>, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.</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 P𝓁n is expressed as a linear combination of Pmn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R = 2r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.

Summing a Family of Generalized Pell Numbers

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Summing a Family of Generalized Pell Numbers"}

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...

Summing a Family of Generalized Pell Numbers

Published Online: Dec 14, 2020

Page range: 105 - 112

Received: Oct 28, 2020

Accepted: Nov 19, 2020

DOI: https://doi.org/10.2478/amsil-2020-0024

Keywords
Pell numbers, Binet formula, generating functions

© 2020 Helmut Prodinger, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Summing a Family of Generalized Pell Numbers

Published Online: Dec 14, 2020

Page range: 105 - 112

Received: Oct 28, 2020

Accepted: Nov 19, 2020

DOI: https://doi.org/10.2478/amsil-2020-0024

KeywordsPell numbers, Binet formula, generating functions

© 2020 Helmut Prodinger, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Pell numbers, Binet formula, generating functions