A Study on Generalized Blaise Numbers
Yüksel Soykan *
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, Zonguldak-67100, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce and investigate the generalized Blaise sequences and we deal with, in detail, two special cases, namely, Blaise and Blaise-Lucas sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Furthermore, we show that there are close relations between Blaise, Blaise-Lucas and Jacobsthal-Padovan, Jacobsthal-Perrin, adjusted Jacobsthal-Padovan, modified Jacobsthal-Padovan numbers. Moreover, we give some identities and matrices related with these sequences.
Keywords: Blaise numbers, Blaise-Lucas numbers, Jacobsthal-Padovan numbers, Jacobsthal-Perrin numbers, adjusted Jacobsthal-Padovan numbers, modified Jacobsthal-Padovan numbers