Description

• Title:
  On generalized Jacobsthal and Jacobsthal-Lucas numbers
• Creator:
  Bród, Dorota;
  Michalski, Adrian
• Description:
  Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers. We define two sequences, called generalized Jacobsthal sequence and generalized Jacobsthal–Lucas sequence. We give generating functions, Binet’s formulas for these numbers. Moreover, we obtain some identities, among others Catalan’s, Cassini’s identities and summation formulas for the generalized Jacobsthal numbers and the generalized Jacobsthal–Lucas numbers. These properties generalize the well-known results for classical Jacobsthal numbers and Jacobsthal–Lucas numbers. Additionally, we give a matrix representation of the presented numbers.
• Object availability:
  free access
• Rights: http://creativecommons.org/licenses/by/4.0
• Date:
  2022.07.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 36 No 2 (2022); 115-128;
  Annales Mathematicae Silesianae; Tom 36 Nr 2 (2022); 115-128;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13894/10581
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13894
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  check license
• Type:
  other