On the properties of Lucas numbers with binomial coefficients (original) (raw)
Abstract
In this study, some new properties of Lucas numbers with binomial coefficients have been obtained to write Lucas sequences in a new direct way. In addition, some important consequences of these results related to the Fibonacci numbers have been given.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
References (12)
- V.E. Hoggat, Fibonacci and Lucas Numbers, Palo Alto, CA, Houghton, 1969.
- S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section, Theory and Applications, John Wiley and Sons, New York, 1989.
- Arthur T. Benjamin, Jennifer J. Quinn, Francis Edward Su, Phased tilings and generalized Fibonacci identities, Fibonacci Quarterly 38 (3) (2000) 282-288.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., NY, 2001.
- A. Stakhov, Fibonacci matrices, a generalization of the 'Cassini formula', and a new coding theory, Chaos, Solitons & Fractals 30 (2006) 56-66.
- M.S. El Naschie, The golden mean in quantum geometry, Knot theory and related topics, Chaos, Solutions & Fractals 10 (8) (1999) 1303-7.
- M.S. El Naschie, The Fibonacci code behind super strings and P-Branes, an answer to M. Kakus fundamental question, Chaos, Solutions & Fractals 31 (3) (2007) 537-47.
- L. Marek-Crnjac, On the mass spectrum of the elementary particles of the standard model using El Naschie's golden field theory, Chaos, Solutions & Fractals 15 (4) (2003) 611-8.
- L. Marek-Crnjac, The mass spectrum of high energy elementary particles via El Naschie's golden mean nested oscillators, the Dunkerly-Southwell eigenvalue theorems and KAM, Chaos, Solutions & Fractals 18 (1) (2003) 125-33.
- M.Z. Spivey, Combinatorial sums and finite differences, Discrete Mathematics 307 (2007) 3130-3146.
- S. FalcoĆ, A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solitons & Fractals 33 (1) (2007) 38-49.
- H.H. Gulec, N. Taskara, On the properties of Fibonacci numbers with binomial coefficients, International Journal of Contemporary Mathematical Sciences 4 (25) (2009) 1251-1256.