On ψ-function and two 2-Fibonacci sequences

Krassimir Atanassov and Dimitar Dimitrov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 16, 2010, Number 1, Pages 5–48
Full paper (PDF, 253 Kb)

Details

Authors and affiliations

Krassimir Atanassov
CLBME – Bulgarian Academy of Sciences
P.O.Box 12, Sofia-1113, Bulgaria

Dimitar Dimitrov
CLBME – Bulgarian Academy of Sciences
P.O.Box 12, Sofia-1113, Bulgaria

Abstract

It is shown that the two essential 2-Fibonacci sequences have bases with respect to function ψ with length 24 and their extensions have bases with respect to function ψ with length 216.

Keywords

• Fibonacci sequence
• ψ-function

AMS Classification

• 11B39

References

1. Atanassov, K. An arithmetic function and some of its applications. Bull. of Number Theory and Related Topics, Vol. IX (1985), No. 1, 18-27.
2. Atanassov K., L. Atanassova, D. Sasselov, A new perspective to the generalization of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 23 (1985), No. 1, 21-28.
3. Atanassov K., On a second new generalization of the Fibonacci sequence. The Fibonacci Quarterly, Vol. 24 (1986), No. 4, 362-365.
4. Lee J.-Z., J.-S. Lee, Some properties of the generalization of the Fibonacci sequence. The Fibonacci Quarterly, Vol. 25 (1987) No. 2, 111-117.
5. Shannon A., R. Melham, Carlitz generalizations of Lucas and Lehmer sequences, The Fibonacci Quarterly, Vol. 31 (1993), No. 2, 105-111.