The Fibonacci p-numbers and Pascal's triangle

Pascal's triangle is the most famous of all number arrays full of patterns and surprises. It is well known that the Fibonacci numbers can be read from Pascal's triangle. In this paper, we consider the Fibonacci p-numbers and derive an explicit formula for these numbers by using some properties of the Pascal's triangle. We also introduce the companion matrix of the Fibonacci p-numbers and give some identities of the Fibonacci p-numbers by using some properties of our matrix.