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New generalizations and identities of Mersenne-Lucas numbers and polynomials with structural constraints | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 اردیبهشت 1405 اصل مقاله (443.44 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30674.2571 | ||
| نویسندگان | ||
| Kalika Prasad1؛ Mritunjay Kumar Singh2؛ Munesh Kumari* 1 | ||
| 1Department of Mathematics, Government Engineering College Bhojpur, Bihar, India | ||
| 2Government Polytechnic, Nawada, Bihar, 805122, India | ||
| چکیده | ||
| This paper introduces and investigates two new sequences, $\{R_{n}^{(k)}\}$ and $\{R_{n}^{(k)}(x)\}$, which provide a distinct generalization of the Mersenne--Lucas numbers and polynomials, respectively, where the index $n$ is expressed in the form $n = sk + r$, with $0 \le r < k$. We derive several identities for these sequences in relation to the classical Mersenne and Mersenne--Lucas numbers and polynomials. Furthermore, we examine their algebraic properties and establish connections with existing sequences and polynomial families. In addition, we obtain closed-form expressions, Cassini-type identities, partial sums, recurrence relations, and various combinatorial identities associated with these sequences. | ||
| کلیدواژهها | ||
| Mersenne-Lucas numbers؛ Mersenne polynomials؛ Mersenne-Lucas polynomials؛ recurrence relation | ||
| مراجع | ||
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