On a four-parameter generalization of some special sequences

被引：7
作者：
da Silva, Robson [1 ]
de Oliveira, Kelvin Souza [2 ]
da Graca Neto, Almir Cunha [3 ]
机构：
[1] Univ Fed Sao Paulo, BR-12247014 Sao Jose Dos Campos, SP, Brazil
[2] Univ Fed Amazonas, BR-69103128 Manaus, Amazonas, Brazil
[3] Univ Estado Amazonas, BR-69055038 Manaus, Amazonas, Brazil
来源：
DISCRETE APPLIED MATHEMATICS | 2018年 / 243卷
关键词：
Generalized Fibonacci numbers; Generalized Lucas numbers; Tilings; Identities; FIBONACCI NUMBERS; LUCAS-NUMBERS; PELL NUMBERS; IDENTITIES; GRAPHS;
D O I：
10.1016/j.dam.2018.03.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a new four-parameter sequence that simultaneously generalizes some well-known integer sequences, including Fibonacci, Padovan, Jacobsthal, Pell, and Lucas numbers. Combinatorial interpretations are discussed and many identities for this general sequence are derived. As a consequence, a number of identities for Fibonacci, Lucas, Pell, Jacobsthal, Padovan, and Narayana numbers as well as some of their generalizations are obtained. We also present the Cassini formula for the new sequence. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：154 / 171
页数：18
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