On sums of odd and even terms of the K-Fibonacci numbers
Abstract
In this paper, we define some properties of sums of k-Fibonacci numbers. Also we present the sum of consecutive members of k-Fibonacci numbers and the same thing for even and for odd k-Fibonacci numbers. Mainly, Binet’s formula will be used to establish properties of k-Fibonacci numbers.
Keywords: K-Fibonacci Numbers, K-Lucas Numbers, Binet’s Formula.
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References
[1] A. Chen and H. Chen, "Identities for the Fibonacci Powers", International Journal of Mathemtical Education 39(4) (2008), 534-541.
[2] A. T. Benjamin and J. J. Quinn, “Recounting Fibonacci and Lucas identities”, College Math. J., 30(5): (1999), 359-366.
[3] D. Kalman, R. Mena, The Fibonacci numbers - exposed. Math Mag., 76 (2003), 167–81.
[4] D. Jennings, "On sums the reciprocals of Fibonacci and Lucas Numbers", The Fibonacci Quarterly, 32(1) (1994), 18-21.
[5] H. Belbachir and F. Bencherif, “Sums of products of generalized Fibonacci and Lucas numbers”, arXiv: 0708.2347v1 [math.NT], (2007).
View more references (17)
[6] R. S. Melham, "Sums of certain products of Fbonacci and Lucas Numbers", The Fibonacci Quarterly 37(3) (1999), 248-251.
[7] S. Clarly and D. Hemenway, "On sums of cubes of Fibonacci Numbers", In Applications of Fibonacci Numbers 5 (1993), 123-136.
[8] S. Falco´n, on the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6(21) (2011), 1039-1050.
[9] S. Falco´n, On the Lucas Triangle and its Relationship with the k-Lucas numbers. Journal of Mathematical and Computational Science, 2(3) (2012), 425-434.
[10] S. Falco´n, Plaza, A.: On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32(5) (2007), 1615-1624.
[11] S. Falco´n, Plaza, A.: The k-Fibonacci hyperbolic functions. Chaos, Solitons & Fractals, 38(2) (2008), 409–20.
[12] S. Falco´n, Plaza, A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons &Fractals, 33(1) (2007), 38-49.
[13] S. Vajda, Fibonacci and Lucas numbers, and the golden section. Theory and applications. Chichester: Ellis Horwood limited (1989).
[14] T. Koshy, “Fibonacci and Lucas Numbers with Applications”, A Wiley-Interscience Publication, New York, (2001).
[15] V. E. Hoggat, Fibonacci and Lucas numbers. Palo Alto, CA: Houghton, (1969).
[16] V. Rajesh and G. Leversha, “Some properties of odd terms of the Fibonacci sequence”, Mathematical Gazette, 88(511): (2004), 85–86.
[17] Y. Yazlik, N. Yilmaz and N. Taskara, “On the Sums of Powers of k-Fibonacci and k-Lucas Sequences” Selçuk J. Appl. Math., Special Issue (2012), 47-50.
[18] Z. Čerin, “Alternating sums of Lucas numbers”, Central European Journal of Mathematics, 3(1): (2005), 1-13.
[19] Z. Čerin, “On sums of squares of odd and even terms of the Lucas sequence”, Proceedings of the 11th Fibonacci Conference, (to appear).
[20] Z. Čerin, “Properties of odd and even terms of the Fibonacci sequence”, Demonstratio Mathematica, 39(1): (2006), 55–60.
[21] Z. Čerin and G. M. Gianella, “On sums of Pell numbers”, Acc. Sc. Torino – Atti Sc. Fis. 140, xx-xx. web.math.pmf.unizg.hr/~cerin/c165.pdf, (2006).
[22] Z. Čerin and G. M. Gianella, “On sums of squares of Pell-Lucas numbers”, INTEGERS: Electronic Journal of Combinatorial Number Theory, 6, #A15, (2006).