On two-parameters generalization of Fibonacci numbers

In this paper we introduce  a new two-parameters generalization ofFibonacci numbers - distance s-Fibonacci numbers  F_s(k,n). We generalize known distance Fibonacci numbers by adding an additional integer parameter s. We give combinatorial and graph interpretations of these numbers. Moreover, we present some properties of distance s-Fibonacci numbers, which generalize known properties of classical Fibonacci and Padovan numbers.