Generalized Ernst Numbers
Yüksel Soykan *
Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we define and investigate the generalized Ernst sequences and we deal with, in detail, two special cases, namely, Ernst and Ernst-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 Ernst and Ernst-Lucas numbers and Jacobsthal, Jacobsthal-Lucas numbers.
Keywords: Ernst numbers, Ernst-Lucas numbers, Tribonacci numbers, Jacobsthal numbers, Jacobsthal- Lucas numbers
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References
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