Fibonacci Generating Functions

被引：0

作者：

Knapp, Michael P. ^{[1
]}

机构：

[1] Loyola Univ Maryland, Dept Math & Stat, 4501 North Charles St, Baltimore, MD 21210 USA

来源：

JOURNAL OF INTEGER SEQUENCES | 2024年 / 27卷 / 03期

关键词：

generating function; Fibonacci recurrence;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Define an integer sequence (G(n))(n is an element of Z) by setting G(0) = a, G(1) = b, and G(n) = G(n-1) + G(n-2) for all n. In this paper, we explore the problem of finding all rational numbers x such that the generating function of the sequence yields an integer when evaluated at x. We show that these numbers can be naturally divided into families and find some families that are always present. Then we give an algorithm that, for each choice of a and b, reduces the problem of finding all of the families to a finite computation.

引用

页码：1 / 12

页数：12

共 50 条

[31] Generating functions and congruences for some partition functions related to mock theta functions
Baruah, Nayandeep Deka
Begum, Nilufar Mana
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2020, 16 (02) : 423 - 446
[32] Generating functions for multi-labeled trees
Czabarka, E.
Erdos, P. L.
Johnson, V.
Moulton, V.
DISCRETE APPLIED MATHEMATICS, 2013, 161 (1-2) : 107 - 117
[33] Beta-type polynomials and their generating functions
Simsek, Yilmaz
APPLIED MATHEMATICS AND COMPUTATION, 2015, 254 : 172 - 182
[34] Generating functions of the Cauchy operator of a hamiltonian system
Shmyrov, A. S.
Shmyrov, V. A.
Shymanchuk, D. V.
VESTNIK SANKT-PETERBURGSKOGO UNIVERSITETA SERIYA 10 PRIKLADNAYA MATEMATIKA INFORMATIKA PROTSESSY UPRAVLENIYA, 2023, 19 (04): : 522 - 528
[35] Powers of Catalan generating functions for bounded operators
Miana, Pedro J. J.
Romero, Natalia
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (12) : 13262 - 13278
[36] New Method for the Computation of Generating Functions with Applications
Zhang, Jun
Fan, Ruzong
Shen, Fangyang
2021 INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE AND COMPUTATIONAL INTELLIGENCE (CSCI 2021), 2021, : 544 - 549
[37] Generating functions for the numbers of pyramid and staircase polyhedra
Chen, M
Lin, KY
MODERN PHYSICS LETTERS B, 2004, 18 (11): : 493 - 500
[38] Some Generating Functions for a Class of Hypergeometric Polynomials
Ozmen, Nejla
Erkus Duman, Esra
GAZI UNIVERSITY JOURNAL OF SCIENCE, 2018, 31 (04): : 1179 - 1190
[39] Coefficient Asymptotics of Algebraic Multivariable Generating Functions
Baryshnikov Y.
Jin K.
Pemantle R.
La Matematica, 2024, 3 (1): : 293 - 336
[40] Determinants of some Hessenberg matrices with generating functions
Leerawat, Utsanee
Daowsud, Katthaleeya
SPECIAL MATRICES, 2023, 11 (01): : 1 - 8

← 1 2 3 4 5 →