C. N. Phadte and S. P. Pethe

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 3, Pages 70—76

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## Details

### Authors and affiliations

C. N. Phadte

*Department of Mathematics, Goa University
Taleigao Goa, India
*

S. P. Pethe

*Dr. Flat No.1 Premsagar Society
Mahatmanagar, Road D-2, Nasik-442007, India
*

### Abstract

In this paper, we establish some results about second order non homogeneous recurrence relation containing extended trignometric function. Earlier {4}, we proved some properties of recurrence relation

g_{n+2} = g_{n+1} + g_{n} + At^{n}, n = 0, 1, … with g_{0} = 0, g_{1} = 1; where both A ≠ 0 and t ≠ 0, and also t ≠ α, β where α, β are the roots of x^{2} − x − 1 = 0.

Using the properties of generalised circular functions and Elmore’s method, we define a new sequence {H_{n}} which is the extension of Pseudo Fibonacci Sequence, given by recurrence relation

H_{n+2} = pH_{n+1} − qH_{n} + Rt^{n}N_{r,0}(t^{*}x),

where N_{r,0}(t^{*}x) is extended circular function.

We state and prove some properties for this extended Pseudo Fibonacci Sequence {H_{n}}.

### Keywords

- Pseudo Fibonacci Sequence
- Non-homogeneous recurrence relation

### AMS Classification

- 11B39

### References

- Elmore, M. (1967) Fibonacci functions, Fibonacci Quarterly 4, 5, 371–382.
- Mikusinski, J. G. (1948) Sur les Fonctions, Annales da la Societe Polonaize de Mathematique, 21, 46–51.
- Horadam, A. F. (1965) Basic Property of a certain Generalized Sequence of Numbers, Fibonacci Quarterly, 3(3), 161–176.
- Phadte, C. N., & Pethe S. P. (2013) On Second Order Non-Homogeneous Recurrence Relation, Annales Mathematicae et Informaticae 41, 205–210.
- Pethe, S. P., & Phadte C. N. (1993) Generalization of the Fibonacci Sequence, Applications of Fibonacci Numbers, Kluwer Academic Pub., 5, 465–472.
- Walton, J. E., & Horadam A. F. (1974) Some Aspect of Fibonacci Numbers. The Fibonacci Quarterly, 12(3), 241–250.

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## Cite this paper

APAPhadte, C. N. & Pethe, S. P. (2015). Trigonometric Pseudo Fibonacci Sequence. Notes on Number Theory and Discrete Mathematics, 21(3), 70-76.

ChicagoPhadte, C. N., and S. P. Pethe. “Trigonometric Pseudo Fibonacci Sequence.” Notes on Number Theory and Discrete Mathematics 21, no. 3 (2015): 70-76.

MLAPhadte, C. N., and S. P. Pethe. “Trigonometric Pseudo Fibonacci Sequence.” Notes on Number Theory and Discrete Mathematics 21.3 (2015): 70-76. Print.