Linear recurrences associated to rays in Pascal's triangle and combinatorial identities

被引：27

作者：

Belbachir, Hacene ^{[1
]}

Komatsu, Takao ^{[2
]}

Szalay, Laszlo ^{[3
]}

机构：

[1] USTHB, Fac Math, Algiers 16111, Algeria

[2] Hirosaki Univ, Dept Math Sci, Hirosaki, Aomori 0368561, Japan

[3] Univ West Hungary, Inst Math, H-9400 Sopron, Hungary

来源：

MATHEMATICA SLOVACA | 2014年 / 64卷 / 02期

基金：

日本学术振兴会;

关键词：

Pascal triangles; linear recurrences; combinatorial properties; CHEBYSHEV;

D O I：

10.2478/s12175-014-0203-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal's triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108-121]. Further, using Morgan-Voyce sequence, we establish the nice identity of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given.

引用

页码：287 / 300

页数：14