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CATALAN TRANSFORM OF THE κ-FIBONACCI SEQUENCE
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 Title & Authors
CATALAN TRANSFORM OF THE κ-FIBONACCI SEQUENCE
Falcon, Sergio;
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 Abstract
In this paper we apply the Catalan transform to the -Fibonacci sequence finding different integer sequences, some of which are indexed in OEIS and others not. After we apply the Hankel transform to the Catalan transform of the -Fibonacci sequence and obtain an unusual property.
 Keywords
-Fibonacci numbers;Catalan numbers;Catalan transform;Hankel transform;
 Language
English
 Cited by
 References
1.
P. Barry, A Catalan transform and related transformations on integer sequences, J. Integer Seq. 8 (2005), no. 4, Article 05.4.5, 24 pp.

2.
A. Cvetkovic, R. Rajkovic, and M. Ivkovic, Catalan numbers, and Hankel transform, and Fibonacci numbers, J. Integer Seq. 5 (2002), no. 1, Article 02.1.3, 8 pp.

3.
S. Falcon and A. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals 32 (2007), no. 5, 1615-1624. crossref(new window)

4.
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)

5.
S. Falcon and A. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals 38 (2008), no. 2, 409-420. crossref(new window)

6.
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison Wesley Publishing Co., 1998.

7.
V. E. Hoggat, Fibonacci and Lucas Numbers, Palo Alto, CA., Houghton-Mifflin, 1969.

8.
A. F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly 68 (1961), 455-459. crossref(new window)

9.
J. W. Layman, The Hankel transform and some of its properties, J. Integer Seq. 4 (2001), no. 1, Article 01.1.5, 11 pp.

10.
M. S. El Naschie, Modular groups in Cantorian $E^{({\infty})}$ high-energy physics, Chaos Solitons Fractals 16 (2003), no. 2, 353-366. crossref(new window)

11.
M. S. El Naschie, The Golden mean in quantum geometry, knot theory and related topics, Chaos Solitons Fractals 10 (1999), no. 8, 1303-1307. crossref(new window)

12.
M. S. El Naschie, Notes on superstrings and the infinite sums of Fibonacci and Lucas numbers, Chaos Solitons Fractals 12 (2001), no. 10, 1937-1940. crossref(new window)

13.
M. S. El Naschie, Topics in the mathematical physics of E-infinity theory, Chaos Solitons Fractals 30 (2006), no. 3, 656-663. crossref(new window)

14.
P. M. Rajkovic, M. D. Petkovic, and P. Barry, The Hankel transform of the sum of consecutive generalized Catalan numbers, Integral Transforms Spec. Funct. 18 (2007), no. 4, 285-296. crossref(new window)

15.
N. J. A. Sloane, The on-line encyclopedia of integer sequences, www.research.att.com/-njas/sequences/

16.
V. W. de Spinadel, The metallic means family and forbidden symmetries, Int. Math. J. 2 (2002), no. 3, 279-288.

17.
R. Stanley and E. W. Weisstein, Catalan Number, From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/CatalanNumber.html.

18.
S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section, Ellis Horwood limited, 1989.

19.
http://en.wikipedia.org/wiki/Catalan_number