On k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers

In this paper, we consider the k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. We obtain the Binet formulas, generating functions, exponential generating functions and summation formulas of k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. Also, we give Catalan, Cassini and d'Ocagne ident...

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Published in:Journal of discrete mathematical sciences & cryptography Vol. 24; no. 4; pp. 1063 - 1074
Main Author: Kilic, Nayil
Format: Journal Article
Language:English
Published: Taylor & Francis 19.05.2021
Subjects:
Fibonacci and Lucas numbers and polynomials and generalizations
Generating functions
Recurrences
ISSN:0972-0529, 2169-0065
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Abstract In this paper, we consider the k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. We obtain the Binet formulas, generating functions, exponential generating functions and summation formulas of k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. Also, we give Catalan, Cassini and d'Ocagne identities of these hybrid numbers. Finally, we introduce the matrix generators for k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers.
AbstractList In this paper, we consider the k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. We obtain the Binet formulas, generating functions, exponential generating functions and summation formulas of k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. Also, we give Catalan, Cassini and d'Ocagne identities of these hybrid numbers. Finally, we introduce the matrix generators for k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers.
Author Kilic, Nayil
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10.1080/09720529.2018.1478628
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10.2478/amsil-2018-0009
10.1007/s00006-018-0833-3
10.1002/9781118033067
10.1002/9781118742297
10.3390/sym11060782
10.1016/j.chaos.2019.109449
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SubjectTerms Fibonacci and Lucas numbers and polynomials and generalizations
Generating functions
Recurrences
Title On k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers
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