181 Downloads 378 Views
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
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 Fibonacci-Like sequences which are similar to Fibonacci sequences in recurrence relation, but initial conditions are different. Due to this reason, these are known as Fibonacci-Like sequences. In this paper, we study a Generalized Fibonacci-Like sequence with initial condition R0=2b and R1= a+b, where a and b are non-zero real numbers. Some identities are established by Binet’s formula and generating function. Further, present connection formulae and some determinant identities.
Fibonacci sequence; Lucas sequence; Fibonacci-Like sequence; Generalized Fibonacci-Like sequence.
Cite this paper
G.P.S. Rathore, Omprakash Sikhwal, Ritu Choudhary, Generalized Fibonacci-Like Sequence and Some Identities, SCIREA Journal of Mathematics. Vol. 1 , No. 1 , 2016 , pp. 107 - 118 .
|[ 1 ]||A. F. Horadam: A Generalized Fibonacci sequence, American Mathematical Monthly, Vol. 68. (5), 1961, 455-459.|
|[ 2 ]||A. F. Horadam: Basic Properties of a Certain Generalized Sequence of Numbers, The Fibonacci Quarterly, Vol. 3 (3), 1965, 161-176.|
|[ 3 ]||B. Singh, O. Sikhwal and S. Bhatnagar: Fibonacci-Like Sequence and its Properties, Int. J. Contemp. Math. Sciences, Vol. 5 (18), 2010, 859-868.|
|[ 4 ]||B. Singh, S. Bhatnagar and O. Sikhwal: Fibonacci-Like Sequence, International Journal of Advanced Mathematical Sciences, 1 (3) (2013), 145-151.|
|[ 5 ]||B. Singh, S. Bhatnagar and O. Sikhwal: Generalized Identties of Companion Fibonacci-Like Sequences, Global Journal of Mathematical Analysis, 1 (3) 2013, 104-109|
|[ 6 ]||L.R. Natividad, Deriving a formula in solving Fibonacci-like sequence, International Journal of Mathematics and Scientific Computing, 1(1) (2011), 19-21.|
|[ 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).|