On Generalized Grahaml Numbers
Yuksel 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 introduce the generalized Grahaml sequences and we deal with, in detail, three special cases which we call them Grahaml, Grahaml-Lucas and modified Grahaml 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.
Keywords: Fibonacci numbers, Grahaml numbers, Grahaml-Lucas numbers, 3-primes numbers, Lucas 3-primes numbers, Tribonacci numbers.