In this study defining Shifted Euler-Seidel matrices we generalize the Euler-Seidel matrices method. Owing to this generalization one can investigate any sequences. (s(n)) which have two term linear recurrences as s(m+n) = alpha s(m+n-1) + beta s(n-1) (alpha and beta are real parameters and n, m is an element of Z(+)). By way of illustration, we give some examples related to the Fibonacci p-numbers.
