The Fibonacci p-numbers and Pascal's triangle

被引：3
|
作者：
Kuhapatanakul, Kantaphon [1 ]
机构：
[1] Kasetsart Univ, Dept Math, Fac Sci, Bangkok 10900, Thailand
来源：
COGENT MATHEMATICS | 2016年 / 3卷
关键词：
Fibonacci p-numbers; Pascal's triangle; Fibonacci p-matrix; Fibonacci p-triangle;
D O I：
10.1080/23311835.2016.1264176
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Pascal's triangle is the most famous of all number arrays full of patterns and surprises. It is well known that the Fibonacci numbers can be read from Pascal's triangle. In this paper, we consider the Fibonacci p-numbers and derive an explicit formula for these numbers by using some properties of the Pascal's triangle. We also introduce the companion matrix of the Fibonacci p-numbers and give some identities of the Fibonacci p-numbers by using some properties of our matrix.
引用
下载
收藏
页数：7
相关论文
共 50 条
  • [21] The Pascal-Fibonacci numbers
    Leyendekkers, J. V.
    Shannon, A. G.
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2013, 19 (03) : 5 - 11
  • [22] SOME PROPERTIES OF THE FIBONACCI-PASCAL TRIANGLE
    Sonrod, Earth
    Tanner, Kate
    Leyner, Colin
    FIBONACCI QUARTERLY, 2022, 60 (05): : 372 - 383
  • [23] ON SOME PROPERTIES OF FIBONACCI DIAGONALS IN PASCAL TRIANGLE
    CASSIDY, C
    HODGSON, BR
    FIBONACCI QUARTERLY, 1994, 32 (02): : 145 - 152
  • [24] On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices
    Kilic, E.
    Stakhov, A. P.
    CHAOS SOLITONS & FRACTALS, 2009, 40 (05) : 2210 - 2221
  • [25] ON A GENERALIZATION OF A LUCAS' RESULT ON THE PASCAL'S TRIANGLE AND MERSENNE NUMBERS
    Yamagami, Atsushi
    Harada, Hideyuki
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2019, 42 (02): : 159 - 169
  • [26] Multiperfect numbers on lines of the Pascal triangle
    Luca, Florian
    Luis Varona, Juan
    JOURNAL OF NUMBER THEORY, 2009, 129 (05) : 1136 - 1148
  • [27] On p-adic complementary theorems between Pascal's triangle and the modified Pascal triangle
    Ando, S
    Sato, D
    FIBONACCI QUARTERLY, 2000, 38 (03): : 194 - 200
  • [28] Coding theory on the m-extension of the Fibonacci p-numbers (vol 42, pg 2522, 2009)
    Prasad, Bandhu
    CHAOS SOLITONS & FRACTALS, 2020, 131
  • [29] The k-Fibonacci sequence and the Pascal 2-triangle
    Falcon, Sergio
    Plaza, Angel
    CHAOS SOLITONS & FRACTALS, 2007, 33 (01) : 38 - 49
  • [30] STAR POLYGONS, PASCALS TRIANGLE, AND FIBONACCI NUMBERS
    BUDGOR, AB
    FIBONACCI QUARTERLY, 1980, 18 (03): : 229 - 231
12345