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- Title
The periods of the k-step Fibonacci and k-step Pell sequences in D<sub>2n</sub> x ℤ<sub>2i</sub> and D<sub>2n</sub> x φ ℤ<sub>2i</sub>.
- Authors
Deveci, Ömür; Avcı, Metin; Karaduman, Erdal
- Abstract
The direct product D2n x ℤ2i and the semidirect product D2n x φ ℤ2ifor n, i ≥ 3 are defined by the presentations D2n x ℤ2i = ‹ x, y, z : x² = yn = (xy)² = z2i = [x, z] = [y, z] = e › and D2n x φ ℤ2i = ‹ x, y, z : x² = yn = (xy)² = z2i = e, z-1 xzx = e, z-1 yzy = e ›, respectively. In this paper, we obtain the periods of the k-nacci sequences and the gener- alized order-k Pell sequences in the direct product D2n x ℤ2i and the semidirect product D2n x φ ℤ2i for n, i ≥ 3.
- Subjects
PELL'S equation; FIBONACCI sequence; DIRECT products (Mathematics); CYCLIC groups; NILPOTENT groups
- Publication
Analele Ştiinţifice ale Universităţii 'Al.I. Cuza' din Iaşi. Matematică, 2018, Issue 2, p283
- ISSN
1221-8421
- Publication type
Article