Abstract
The current paper represents a suplement for papers [7] and [8]. Many of the new summation formulae connecting Lucas numbers with binomials are presented here. All these relations are obtained by using definition and simple properties of the so called δ-Lucas numbers.
References
[1] A. T. Benjamin, J. J. Quin, Proofs That Really Count - the Art of Combinatorial Proof, Mathematical Association of America, 2003.Search in Google Scholar
[2] P. Filipponi, Some binomial and Fibonacci identities, Fibonacci Quart. 33(3) (1995), 251–257.Search in Google Scholar
[3] R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 2006.Search in Google Scholar
[4] M. A. Khan, H. Kwong, Some binomial identities associated with the generalized natural number sequence, Fibonacci Quart. 49(1) (2011), 57–65.Search in Google Scholar
[5] T. Koshy, Fibonacci and Lucas Numbers with Application, Wiley, New York, 2001.10.1002/9781118033067Search in Google Scholar
[6] S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Dover Press, 2008.Search in Google Scholar
[7] R. Wituła, Binomials transformation formulae of scaled Fibonacci numbers, Fibonacci Quart. (in review).Search in Google Scholar
[8] R. Wituła, D. Słota, δ-Fibonacci numbers, Appl. Anal. Discrete Math. 3 (2009), 310–329.10.2298/AADM0902310WSearch in Google Scholar
© 2013 Roman Wituła, published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.