On the k–Lucas Numbers of Arithmetic Indexes

• 作者: Sergio Falcon
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: k–Fibonacci NUMBERS k–Lucas NUMBERS GENERATING FUNCTION
• 年，卷（期）: 2012,（10）
• 页码范围: 1202-1206
• 页数: 5页
• 分类号: O1

摘要

In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.