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
相关论文
共 50 条
  • [41] Two integer sequences related to Catalan numbers
    Lassalle, Michel
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (04) : 923 - 935
  • [42] Congruences related to dual sequences and Catalan numbers
    Wang, Rong-Hua
    Zhong, Michael X. X.
    EUROPEAN JOURNAL OF COMBINATORICS, 2022, 101
  • [43] Angle measurement by comparing the amplitude technique of the sum-difference pattern radiometer
    Wang, Hong
    Xiao, Jing
    Bi, Bo
    CIVIL, ARCHITECTURE AND ENVIRONMENTAL ENGINEERING, VOLS 1 AND 2, 2017, : 775 - 779
  • [44] Sum-Difference Equation for Analytic Functions Generated by Pentagon and Its Application
    Aksenteva, E. P.
    Garifyanov, F. N.
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2016, 37 (02) : 101 - 104
  • [45] Angle Estimation Approach and Performance Analysis for STAP with Sum-Difference Antenna
    Kan Q.-Y.
    Xu J.-W.
    Liao G.-S.
    Tien Tzu Hsueh Pao/Acta Electronica Sinica, 2023, 51 (01): : 42 - 49
  • [46] Ascent sequences and the binomial convolution of Catalan numbers
    Pudwell, Lara K.
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2016, 64 : 21 - 43
  • [47] Integro-Differential Equation with a Sum-Difference Kernels and Power Nonlinearity
    Askhabov, S. N.
    DOKLADY MATHEMATICS, 2022, 106 (03) : 412 - 415
  • [48] Mirrored coprime array design using sum-difference coarray optimisation
    Dai, Minghui
    Ma, Xiaofeng
    Sheng, Weixing
    Han, Yubing
    IET SIGNAL PROCESSING, 2023, 17 (01)
  • [49] Synthesis of compromise sum-difference arrays through time-modulation
    Rocca, P.
    Manica, L.
    Poli, L.
    Massa, A.
    IET RADAR SONAR AND NAVIGATION, 2009, 3 (06): : 630 - 637
  • [50] Sum-Difference Equation for Analytic Functions, Generated by a Hexagon, and Its Applications
    Garifyanov, F. N.
    Strezhneva, E. V.
    RUSSIAN MATHEMATICS, 2020, 64 (07) : 48 - 53
12345