Characterization of linear recurrences associated to rays in Pascal's triangle

被引：7
作者：
Belbachir, Hacene [1 ]
Komatsu, Takao [2 ]
Szalay, Laszlo [3 ]
机构：
[1] USTHB, Fac Math, Po Box 32, Algiers 16111, Algeria
[2] Hirosaki Univ, Dept Math Sci, Hirosaki, Aomori 0368561, Japan
[3] Univ W Hungary, Inst Math & Stat, H-9400 Sopron, Hungary
来源：
DIOPHANTINE ANALYSIS AND RELATED FIELDS 2010 | 2010年 / 1264卷
基金：
日本学术振兴会;
关键词：
Linear recurrence sequences; Fibonacci numbers and polynomials; Pascal triangle; Morgon-Voyce sequence; continued fractions; combinatorial sums; CHEBYSHEV;
D O I：
10.1063/1.3478184
中图分类号：
O59 [应用物理学];
学科分类号：
摘要：
Our purpose is to describe the recurrence relations associated to the sum of diagonal elements laying along a finite ray crossing Pascal's triangle. We also answer Horadam's question posed in his paper entitled Chebyshev and Pell connections, Fibonacci Quart., (2005). Further, using Morgan-Voyce sequence, we establish the nice identity Fn+1 - iF(n) = i(n) Sigma(n)(k=0) ((n+k)2k) (-2 -i)(k) of Fibonacci numbers, where i = root-1. Finally, connections to continued fractions, bivariate polynomials and finite differences are given.
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页码：90 / +
页数：2
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