FACTORIZATIONS OF THE PASCAL MATRIX VIA A GENERALIZED SECOND ORDER RECURRENT MATRIX

Kilic E., ÖMÜR N., TATAR G., ULUTAS Y.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.38, no.3, pp.305-316, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 3
  • Publication Date: 2009
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.305-316
  • Kocaeli University Affiliated: Yes

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.