A new family of k-Fibonacci numbers

作者：El Mikkawy Moawwad^*; Sogabe Tomohiro

来源：Applied Mathematics and Computation, 2010, 215(12): 4456-4461.

DOI：10.1016/j.amc.2009.12.069

• Fibonacci numbers
• Generalized k-Fibonacci numbers
• k-Tridiagonal matrix
• Determinant
• Generating functions
• Recurrence relation

In the present paper, we give a new family of k-Fibonacci numbers and establish some properties of the relation to the ordinary Fibonacci numbers. Furthermore, we describe the recurrence relations and the generating functions of the new family for k = 2 and k = 3, and presents a few identity formulas for the family and the ordinary Fibonacci numbers.

• 出版日期2010-2-15