THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS

Kalika Prasad; Munesh Kumari; Hrishikesh Mahato

THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS

Abstract

In this paper, we investigate the binomial transform and the Catalan transform of the $k$-Leonardo numbers and examine the new integer sequences. We apply the $k$-binomial, rising $k$-binomial, and falling $k$-binomial transforms to the $k$-Leonardo sequences. Further, we study the associated generating and exponential generating functions for these transforms. Finally, we implement the Hankel transform on the Catalan transforms of the $k$-Leonardo numbers to obtain the determinant of Hankel sub-matrices.

Keywords

Thanks

The authors are thankful to the anonymous reviewers for their advice and fruitful corrections.

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory, Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Kalika Prasad
0000-0002-3653-5854
India

Munesh Kumari ^*
0000-0002-6541-0284
India

Hrishikesh Mahato
0000-0002-3769-0653
India

Publication Date

November 3, 2025

Submission Date

December 12, 2024

Acceptance Date

March 31, 2025

Published in Issue

Year 2025 Volume: 15 Number: 11

IZ

https://izlik.org/JA79ZY72LU

Cite

RIS / Bibtex

APA

Prasad, K., Kumari, M., & Mahato, H. (2025). THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS. TWMS Journal of Applied and Engineering Mathematics, 15(11), 2652-2663. https://izlik.org/JA79ZY72LU

AMA

1.Prasad K, Kumari M, Mahato H. THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS. JAEM. 2025;15(11):2652-2663. https://izlik.org/JA79ZY72LU

Chicago

Prasad, Kalika, Munesh Kumari, and Hrishikesh Mahato. 2025. “THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS”. TWMS Journal of Applied and Engineering Mathematics 15 (11): 2652-63. https://izlik.org/JA79ZY72LU.

EndNote

Prasad K, Kumari M, Mahato H (November 1, 2025) THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS. TWMS Journal of Applied and Engineering Mathematics 15 11 2652–2663.

IEEE

[1]K. Prasad, M. Kumari, and H. Mahato, “THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS”, JAEM, vol. 15, no. 11, pp. 2652–2663, Nov. 2025, [Online]. Available: https://izlik.org/JA79ZY72LU

ISNAD

Prasad, Kalika - Kumari, Munesh - Mahato, Hrishikesh. “THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS”. TWMS Journal of Applied and Engineering Mathematics 15/11 (November 1, 2025): 2652-2663. https://izlik.org/JA79ZY72LU.

JAMA

1.Prasad K, Kumari M, Mahato H. THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS. JAEM. 2025;15:2652–2663.

MLA

Prasad, Kalika, et al. “THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 11, Nov. 2025, pp. 2652-63, https://izlik.org/JA79ZY72LU.

Vancouver

1.Kalika Prasad, Munesh Kumari, Hrishikesh Mahato. THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS. JAEM [Internet]. 2025 Nov. 1;15(11):2652-63. Available from: https://izlik.org/JA79ZY72LU