Generalized Pascal matrix and recurrence sequences Original Research Article

This paper gives a product formula of the generalized Pascal matrix φn[x,y], from this, getting the striking simplicity of the powers of φn[x,y]. Furthermore, this paper defines the IEGP-matrix Ωn[x,y]. It is shown that not only can Ωn[x,y] be factorized by special summation matrices, but also has the closely relation with generalized Fibonacci sequences Wn(x,y), an explicit diagonalization of Ωn[x,y] is given.