Factorizations of the Pascal Matrix Via a Generalized Second Order Recurrent Matrix

Abstract

In this paper, we consider positively and negatively subscripted terms of a generalized binary sequence {U-n} with indices in arithmetic progression. We give a factorization of the Pascal matrix by a matrix associated with the sequence {U+/-kn} for a fixed positive integer k, generalizing results of Kihc and Tasci, Lee, Kim and Lee; Stanica; and Zhizheng and Wang. Some new factorizations and combinatorial identities are derived as applications. Therefore we generalize the earlier results on the factorizations of the Pascal matrix.