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Combinatorial Formulas Involving Fibonacci Polynomials, Fibonacci-Like Polynomials and Fibonacci-Like Sequences
| National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011 |
| Foundation of Computer Science USA |
| RTMC - Number 2 |
| May 2012 |
| Authors: V. K. Gupta, Omprakash Sikhwal, Yashwant K. Panwar |
V. K. Gupta, Omprakash Sikhwal, Yashwant K. Panwar . Combinatorial Formulas Involving Fibonacci Polynomials, Fibonacci-Like Polynomials and Fibonacci-Like Sequences. National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011. RTMC, 2 (May 2012), 4-6.
Abstract
In this paper, our idea from graphical theory, according to the methods of partial fractions, a great of combinatorial identities related to Fibonacci polynomials and Fibonacci-Like polynomials will be obtained. We shows that some identities between Fibonacci polynomials ? ( )? k k o f x ? and Associated numbers ? (n, k) , Fibonacci-Like polynomials ? ( )? ,? ( )? ,? ( )? ,? ( )? ,? ( )? k k o k k o k k o k k o k k o l x P x Q x J x j x ? ? ? ? ? ? ? ? ? and Associated numbers ? (n, k) , with their generating function, and give several interesting identities involving them.
References
- A. Lupas, A Guide of Fibonacci and Lucas Polynomial, Octagon Mathematics Magazine, Vol. 7, No. 1 (1999), 2-12. .
- A. G. Shannon, A method of Carlitz applied to the k-th power generating function for Fibonacci numbers, Fibonacci Quart. , 12 (1974), 293â299.
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