Theory of Binet formulas for Fibonacci and Lucas p-numbers

被引：94

作者：

Stakhov, A ^{[1
]}

Rozin, B ^{[1
]}

机构：

[1] Int Club Golden Soc, Bolton, ON L7E 2C8, Canada

来源：

CHAOS SOLITONS & FRACTALS | 2006年 / 27卷 / 05期

关键词：

D O I：

10.1016/j.chaos.2005.04.106

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Modern natural science requires the development of new mathematical apparatus. The generalized Fibonacci numbers or Fibonacci p-numbers (p = 0, 1, 2, 3,...), which appear in the "diagonal sums" of Pascal's triangle and are assigned in the recurrent form, are a new mathematical discovery. The purpose of the present article is to derive analytical formulas for the Fibonacci p-numbers. We show that these formulas are similar to the Binet formulas for the classical Fibonacci numbers. Moreover, in this article, there is derived one more class of the recurrent sequences, which is defined to be a generalization of the Lucas numbers (Lucas p-numbers). (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：1162 / 1177

页数：16

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