192 Downloads 437 Views
Author(s)
G.P.S. Rathore, Department of Mathematics, College of Horticulture, Mandsaur, India
Omprakash Sikhwal, Devanshi Tutorial, Keshaw Kunj, Mandsaur (M.P.), India
Ritu Choudhary, School of Studies in Mathematics, Vikram University Ujjain (M.P.), India
Abstract
Sequences have been fascinating topic for mathematicians for centuries. The Fibonacci and Lucas sequences are examples of second order recursive sequences. Fibonacci sequence is defined by In recent years, few research scholars have been introduced FibonacciLike sequences which are similar to Fibonacci sequences in recurrence relation, but initial conditions are different. Due to this reason, these are known as FibonacciLike sequences. In this paper, we study a Generalized FibonacciLike sequence with initial condition R0=2b and R1= a+b, where a and b are nonzero real numbers. Some identities are established by Binetâ€™s formula and generating function. Further, present connection formulae and some determinant identities.
Keywords
Fibonacci sequence; Lucas sequence; FibonacciLike sequence; Generalized FibonacciLike sequence.
Cite this paper
G.P.S. Rathore,
Omprakash Sikhwal,
Ritu Choudhary,
Generalized FibonacciLike Sequence and Some Identities, SCIREA Journal of Mathematics. Vol.
1
, No.
1
,
2016
, pp.
107

118
.
References
[ 1 ]  A. F. Horadam: A Generalized Fibonacci sequence, American Mathematical Monthly, Vol. 68. (5), 1961, 455459. 
[ 2 ]  A. F. Horadam: Basic Properties of a Certain Generalized Sequence of Numbers, The Fibonacci Quarterly, Vol. 3 (3), 1965, 161176. 
[ 3 ]  B. Singh, O. Sikhwal and S. Bhatnagar: FibonacciLike Sequence and its Properties, Int. J. Contemp. Math. Sciences, Vol. 5 (18), 2010, 859868. 
[ 4 ]  B. Singh, S. Bhatnagar and O. Sikhwal: FibonacciLike Sequence, International Journal of Advanced Mathematical Sciences, 1 (3) (2013), 145151. 
[ 5 ]  B. Singh, S. Bhatnagar and O. Sikhwal: Generalized Identties of Companion FibonacciLike Sequences, Global Journal of Mathematical Analysis, 1 (3) 2013, 104109 
[ 6 ]  L.R. Natividad, Deriving a formula in solving Fibonaccilike sequence, International Journal of Mathematics and Scientific Computing, 1(1) (2011), 1921. 
[ 7 ]  O. Sikhwal, Generalization of Fibonacci Sequence: An Intriguing Sequence, Lap Lambert Academic Publishing GmbH & Co. KG, Germany (2012). 
[ 8 ]  T. Koshy ,Fibonacci and Lucas Numbers with Applications, Wiley Interscience Publication, New York (2001). 