JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A NOTE ON THE MODIFIED k-FIBONACCI-LIKE SEQUENCE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A NOTE ON THE MODIFIED k-FIBONACCI-LIKE SEQUENCE
Kwon, Youngwoo;
  PDF(new window)
 Abstract
The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the modified k-Fibonacci-like sequence and prove Binet`s formula for this sequence and then use it to introduce and prove the Catalan, Cassini, and d`Ocagne identities for the modified k-Fibonacci-like sequence. Also, the ordinary generating function of this sequence is stated.
 Keywords
k-Fibonacci sequence;k-Fibonacci-like sequence;Binet`s formula;
 Language
English
 Cited by
 References
1.
V. H. Badshah, M. S. Teeth, and M. M. Dar, Generalized Fibonacci-like sequence and its properties, Int. J. Contemp. Math. Sci. 7 (2012), no. 21-24, 1155-1164.

2.
P. Catarino, On some identities for k-Fibonacci sequence, Int. J. Contemp. Math. Sci. 9 (2014), no. 1, 37-42.

3.
M. Edson, S. Lewis, and O. Yayenie, The k-periodic Fibonacci sequence and an extended Binet's formula, Integers 11 (2011), A32, 12 pp.

4.
M. Edson and O. Yayenie, A new generalization of Fibonacci sequences and extended Binet's formula, Integers 9 (2009), A48, 639-654.

5.
S. Falcon, On the k-Lucas Numbers, Int. J. Contemp. Math. Sci. 6 (2011), no. 21, 1039-1050.

6.
S. Falcon and A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos Solitons Fractals 33 (2007), no. 1, 38-49. crossref(new window)

7.
S. Harne, B. Singh, and S. Pal, Generalized Fibonacci-like sequence and Fibonacci sequence, Int. J. Contemp. Math. Sci. 9 (2014), no. 5, 235-241.

8.
V. E. Hoggat, Fibonacci and Lucas numbers, Palo Alto, CA: Houghton; 1969.

9.
Y. K. Panwar, G. P. S. Rathore, and R. Chawla, On the k-Fibonacci-like numbers, Turkish J. Anal. Number Theory 2 (2014), no. 1, 9-12.

10.
Y. K. Panwar, B. Singh, and V. K. Gupta, Generalized Fibonacci sequence and its properties, Palest. J. Math. 3 (2014), no. 1, 141-147.

11.
B. Singh, O. Sikhwal, and S. Bhatnagar, Fibonacci-like sequence and its properties, Int. J. Contemp. Math. Sci. 5 (2010), no. 17-18, 859-868.

12.
O. Yayenie, A note on generalized Fibonacci sequences, Appl. Math. Comput. 217 (2011), no. 12, 5603-5611.