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Some new families of generalized $k$-Leonardo and Gaussian Leonardo Numbers | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 11، دوره 9، شماره 3، آذر 2024، صفحه 539-553 اصل مقاله (402.27 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28236.1485 | ||
| نویسندگان | ||
| Kalika Prasad؛ Ritanjali Mohanty* ؛ Munesh Kumari؛ Hrishikesh Mahato | ||
| Department of Mathematics, Central University of Jharkhand, India, 835205 | ||
| چکیده | ||
| In this paper, we introduce a new family of the generalized $k$-Leonardo numbers and study their properties. We investigate the Gaussian Leonardo numbers and associated new families of these Gaussian forms. We obtain combinatorial identities like Binet formula, Cassini's identity, partial sum, etc. in the closed form. Moreover, we give various generating and exponential generating functions. | ||
| کلیدواژهها | ||
| k-Leonardo numbers؛ k-Gaussian Leonardo numbers؛ Binet formula؛ Generating functions؛ Partial sum | ||
| مراجع | ||
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