Generalized Friedrich Numbers
Yüksel Soykan *
Department of Mathematics, Faculty of Science, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we define and investigate the generalized Friedrich sequences and we deal with, in detail, two special cases, namely, Friedrich and Friedrich-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between Friedrich, Friedrich-Lucas and third order Jacobsthal, modified third-order Jacobsthal, third order Jacobsthal-Lucas numbers.
Keywords: Friedrich numbers, friedrich-Lucas numbers, Jacobsthal numbers, third order Jacobsthal numbers, modified third-order Jacobsthal numbers, third order Jacobsthal-Lucas numbers