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Research Article Open access CC BY 4.0

On Generalized Grahaml Numbers

Yüksel Soykan

Journal of Advances in Mathematics and Computer Science · pp. 42–57 · Published 14 Mar 2020

10.9734/jamcs/2020/v35i230248

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.

Fibonacci numbers Grahaml numbers Grahaml-Lucas numbers 3-primes numbers Lucas 3-primes numbers Tribonacci numbers.

References (7)

  1. 1 The on-line encyclopedia of integer sequences [DOI]
  2. 2 Summing Formulas for Generalized Tribonacci Numbers [DOI]
  3. 3 Tribonacci and Tribonacci-Lucas numbers via the determinants of special matrices [DOI]
  4. 4 MODULAR TRIBONACCI NUMBERS BY MATRIX METHOD [DOI]
  5. 5 A Matrix Approach for General Higher Order Linear Recurrences
  6. 6 Identities for Tribonacci-related sequences [DOI]
  7. 7 Simson Identity of Generalized m-step Fibonacci Numbers [DOI]

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