Generalized Identities Related for The k-Fibonacci Number, The k-Lucas Number and k-Fibonacci-Like Number
Main Article Content
Abstract
In this paper, we present generalized identities for k-Fibonacci, k-Lucas and k-Fibonacci-Like sequence. We obtain the Binet’s formula for related some identities.
Article Details
References
S. Falcon, On the k-Lucas number, International Journal of Contemporary Mathematical Sciences, Vol. 6, No.21, 2011, pp.1039-1050.
S. Falcon and A. Plaza, On the Fibonacci k-number, Chaos, Solution & Fractal, Vol.32, No. 5, 2007, pp.1615-1625.
A.F. Horadam, The Generalized Fibonacci Sequences, The American Mathematical Monthly, Vol. 68, No. 5 1961, pp.455-459.
A.F. Horadam, Basic Properties of Centain Generalized sequence of Numbers, The Fibonacci Quarterly, Vol.3, No.3, 1965, pp.161-176.
Y.K. Panwar, G.P.S. Rathore and R. Chawla, On the k-Fibonacci-like Number, Turkish Journal of Analysis and Number Theorem, Vol. 2, No. 1, 2014, pp.9-12.
Y. K. Panwar, B. Singh and V.K. Gupta, Generalized Fibonacci Sequences and Its Properties, Palestine Journal of Mathematics, Vol. 3, No. 1, 2014, pp.141-147.
D. M. Mahajan, K. Arcade and B. Nagar, The Binet Forms for the Fibonacci and Lucas Number, International Journal Mathematics Trends and Technology, Vol. 10, No. 1, 2014, pp.14-16.
Y. K. Panwar and M. Singh, k-Generalized Fibonacci Numbers, Applied Mathematics and Physics, Vol. 2, No.1, 2014, pp.10-12.
M. Tatong, T. Ampawa and A. Suvarnamani, On The k-Fibonacci-like Number, The IEEE International Conference on Science and Technology, 7-8 December 2017 Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, pp.528-531.
Y. K. Gupta, M. Singh and O. Sikhwal, Generalized Fibonacci-Like Sequence Associated with Fibonacci and Lucas Sequences, Turkish Journal of Analysis and Number Theorem, Vol. 2, No. 6, 2014, pp.233-238.
Y. K. Panwar and M. Singh, k-Fibonacci number, Applied Mathematics and Physics, Vol. 2, No. 1, 2014, pp.10-12.
A.J. Macfarlane, Use of Determinants to present identities involving Fibonacci and Related number, The Fibonacci Quarterly, Vol. 8, No. 1, 2010, pp.68-76.
A.T. Benjami and J.J. Quinn, Recounting Fibonacci and Lucas identities, College Mathematice Journal, Vol. 30, No. 5, 1999, pp.359-366.
B. Sing , V.K. Gupta and Y.K. Panwar, On Combinations of Higher Powers of Fibonacci – Like sequence, Open Journal of Mathematical Modeling, Vol. 1, No. 2, 2013, pp. 63-66.
D. Kalman and R. Mena, The Fibonacci Numbers-Exposed, The Mathematical Magazine, Vol. 76, No. 3, 2002, pp.60-65.
L.A.G. Dresel, Transformations of Fibonacci-Lucas identities, Applications of Fibonacci Numbers, 1993, pp.169-184.
L.R. Natividad, Deriving a Formula in Solving Fibonacci-like sequence, International Journal of Mathematics and Scientific Computing, Vol. 1, No. 1, 2011, pp.19-21.
V.K. Gupta, Y.K. Panwar and N. gupta, Identities of Fibonacci-Like sequence, Journal of Mathematical and Computational Science, Vol. 2, No. 6, 2012, pp. 1801-1807.
V.K. Gupta, Y.K. Panwar and O. Sikhwal, Generalized fibonacci Sequences, Theoretical Mathematics & Applications, Vol. 2, No. 2, 2012, pp. 115-124.
A. Suvarnamani and M. Tatong, Some Properties of (p,q)-Lucas Number, Science and Technology RMUTT Journal, Vol. 5, No. 2, 2015, pp.17-21.
A. Suvarnamani, On the Odd and Even Tems of (p,q) –Fibonacci number and (p,q) –Lucas number, NSRU Science and Technology Journal, Vol. 8, No. 8, 2016, pp.73-78.