In this work, we define a family of sparse Hessenberg matrices whose perma-nents lead us to k-Fibonacci, Fibonacci-p and Pell (p,i) numbers. Furthermore, we show that it contains some well-known general number sequences in it. We provide a Maple 13 source code describing the contraction steps. Keywords: Determinant, Fibonacci-p and Pell (p,i) numbers, Hessenberg matrix, k-Fibonacci numbers, Permanent.