New Approach to Pell and Pell-Lucas Sequences
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we rst de ne generalizations of Pell and Pell-Lucas sequences by the recurrence relations pn = 2ap_n-1 + (b - a^2)p_n-2 and q_n = 2aq_n-1 + (b - a^2)q_n-2 with initial conditions p0 = 0, p1 = 1, and q0 = 2, q1 = 2a, respectively. We give generating functions and Binet's formulas for these sequences. Also, we obtain some identities of these sequences.
Abstract
In this paper, we rst de ne generalizations of Pell and Pell-Lucas sequences by the recurrence relations pn = 2ap_n-1 + (b - a^2)p_n-2 and q_n = 2aq_n-1 + (b - a^2)q_n-2 with initial conditions p0 = 0, p1 = 1, and q0 = 2, q1 = 2a, respectively. We give generating functions and Binet's formulas for these sequences. Also, we obtain some identities of these sequences.
참고문헌 (9)
- G. Bilgici, "New generalizations of Fibonacci and Lucas sequences", Appl. Math. Sc, 8(29), pp.1429~1437 (2014)
- G. Bilgici, "Two generalizations of Lucas sequence", Appl. Math. Comput, 245, pp.526~538 (2014)
- A. Dasdemir, "On the Pell, Pell-Lucas and modified Pell numbers by matrix method", Appl. Math. Sci, 5(64), pp.3173~3181 (2011)
- M. on, "A new generalization of Fibonacci sequence and extended Binet's formula", Integers, 9, pp.639~654 (2009)
- H. H. Gulec, "On the(s; t)-Pell and(s; t)-Pell-Lucas sequences and their matrix represantations", Appl. Math. Lett, 25, pp.1554~1559 (2012)
- A. F. Horadam, "A generalized Fibonacci sequence", Amer. Math. Monthly, 68, pp.455~459 (1961)
- A. F. Horadam, "Pell identities", Fibonacci Quart, 9(3), pp.245~263 (1971)
- T. Koshy, "Pell and Pell-Lucas numbers with applications" (2014), Springer
- S. P. Pethe, "A generalization of the Fibonacci sequence", Applications of Fibonacci numbers, 5, pp.465~472 (1992)