On the Extended (k, t) - Fibonacci Numbers
Sergio Falcon *
Department of Mathematics, Universidad de as Palmas de Gran Canaria, Spain.
*Author to whom correspondence should be addressed.
Abstract
This article studies an extension of the concept of k-Fibonacci numbers by introducing a new non-zero positive integer parameter t. In case t = 1, the numbers found are the Leonardo numbers. A homogeneous recurrence relationship is found between these new numbers, and various formulas are studied such as the Binet Identity or the generating function.
Keywords: k-Fibonacci numbers, Binet identity, Recurrence relation, Generating function, Leonardo numbers