Sum-difference sequences and Catalan numbers

被引：2

作者：

Aigner, M ^{[1
]}

Schulze, V ^{[1
]}

机构：

[1] Free Univ Berlin, Math Inst 2, D-14195 Berlin, Germany

来源：

MONATSHEFTE FUR MATHEMATIK | 1999年 / 127卷 / 02期

关键词：

Catalan number; sum-difference sequence; Euclidean algorithm;

D O I：

10.1007/s006050050025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let a(1)a(2) ... a(n) be a sequence of natural numbers > 1, and set a(0) = a(n+1) = 1. The sequence is called admissible if a(i) divides a(i-1) + a(i+1) for all i. It is known that the admissible sequences are counted by the Catalan numbers. We present a proof of this fact which, in turn, leads to some interesting combinatorial and number-theoretic questions.

引用

页码：89 / 99

页数：11

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