Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Turkish Journal of Analysis and Number Theory. 2016, 4(4), 113-117
DOI: 10.12691/tjant-4-4-5
Open AccessArticle

Generalization of Horadam’s Sequence

C.N. Phadte1, and Y.S. Valaulikar2

1Department of Mathematics, G.V.M’s College of Commerce & Economics, Ponda, Goa 403401, India

2Department of Mathematics, Goa University Taleigao Plateau, 403206, Goa, India

Pub. Date: September 02, 2016

Cite this paper:
C.N. Phadte and Y.S. Valaulikar. Generalization of Horadam’s Sequence. Turkish Journal of Analysis and Number Theory. 2016; 4(4):113-117. doi: 10.12691/tjant-4-4-5


In this paper a new class of Fibonacci like sequence is introduced. Here we consider non-homogeneous recurrence relation to obtain generalization of Horadam’s Sequence. Some identities concerning this new sequence are obtained and proved. Some examples are given in support of the results.

pseudo fibonacci numbers non-homogeneous recurrence relation

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/


[1]  A. F. Horadam, “A Generalized Sequence of Numbers”, The American Mathematical Monthly, 68 No. 5,(1961), pp.455-459.
[2]  A. F. Horadam, “Basic Properties of a certain Generalized Sequence of Numbers”, The Fibonacci Quarterly, 3, No.3(1965), pp.161-176.
[3]  A. F. Horadam, “Generating functions for power of a certain Generalized Sequence of numbers”, Duke Math J. 32, No.3(1965), pp. 437-446.
[4]  A. F. Horadam, “Special Properties of the Sequence Wn(a,b;p,q)” , The Fibonacci Quarterly, 5, No. 5 (1967), pp. 424-434.
[5]  C. N. Phadte, S.P. Pethe, “Generalization of the Fibonacci Sequence”, Applications of Fibonacci Numbers,5, Kluwer Academic Pub. 1993, 465-472.
[6]  C. N. Phadte, S. P. Pethe, “On Second Order Non-Homogeneous Recurrence Relation”, Annales Mathematicae et Informaticae vol.41 (2013) pp.205-210.
[7]  C. N. Phadte, “Trigonometric Pseudo Fibonacci Sequence”, Notes on Number Theory and Discrete Mathematics,21 No.3, (2015) pp.70-76.
[8]  J. E. Walton, A. F. Horadam, “Some Aspect of Fibonacci Numbers”, The Fibonacci Quarterly, 12.