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
收藏
页码：89 / 99
页数：11
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