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Some relations on Lucas numbers and their sums
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Abstract
In this paper we consider some algebraic properties of Lucas numbers. In the rst section we give some preliminaries from Lucas and Fibonaccinumbers. In the second section, we derive explicit formulas for the Lucas num-bers Ln ;L2n and L2n +1 . In the third section we consider the sums of Lucasnumbers Ln ;L2n and L2n +1 and also their squares. In the third section, wegive another way for the sums of Lucas numbers. In the last section we consider the cross-ratio of four consecutive Lucas numbers Ln ;Ln +1 ;Ln +2 andLn +3 .
참고문헌 (16)
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관련 논문AI추천
On the sequences related to Fibonacci and Lucas numbersNihal Yilmaz Ä, OzgÄ, ur대한수학회 · 대한수학회지2005 · 제42권 제1호Some computational formulas of mixed-convoluted sum for Fibonacci and Lucas sequencesG. Xi, Z. Zhang장전수학회 · Advanced Studies in Contemporary Mathematics2007 · 제14권 제2호Some Properties of (p, q) - Lucas NumberAlongkot Suvarnamani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호GENERALIZING SOME FIBONACCI-LUCAS RELATIONS박호, Jongmin Lee, Junghyun Hong대한수학회 · 대한수학회논문집2023 · 제38권 제1호Lucas-Euler Relations Using Balancing and Lucas-Balancing PolynomialsRobert Frontczak, TARAS GOY경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제3호A complete formula for the order of appearance of the powers of Lucas numbersPrapanpong Pongsriiam대한수학회 · 대한수학회논문집2016 · 제31권 제3호
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