On Some Identites and Generating Functions for (s,t)-Pell and (s,t)-Pell-Lucas Numbers
Main Article Content
Abstract
In this paper, we obtain the Binet’s formula for (s,t)-Pell and (s,t)-Pell-Lucas numbers and then we get some identities for these numbers by using the Binet’s formula. Moreover, we obtain the generating functions for (s,t)-Pell and (s,t)-Pell-Lucas sequences and another expression for the general term of the sequences by using the ordinary generating functions.
Article Details
References
P. Catarino, P. Vasco. Some Basic Properties and a Two- by-Two Matrix Involving the k-Pell Numbers. Int. Journal of Math. Analysis. 7 (5) (2013): 2209–2215.
H.H. Gulec and N. Taskara. On the (s, t)-Pell and (s, t)-Pell Lucas sequences and their matrix representations. Applied Mathematics Letters. 25 (2012): 1554-1559.
A.F. Horadam, Jacobsthal. Representation Numbers. The Fibonacci Quarterly. 34 (1996): 40–54.
A. F. Horadam. Pell identities. The Fibonacci Quarterly. 9 (3) (1971): 245–252.
E. Kl. The generalized Pell (p, i)-numbers and their Binet formulas. Combinatorial representations, sums, Chaos, Solitons Fractals. 40 (2009): 2047–2063.
T. Koshy. Pell and Pell-Lucas Numbers with Applications. Springer. Berlin ; 2014
T. Koshy. Fibonacci and Lucas Numbers with Applications. New York: John Wiley and Sons; 2001.
M.S. El Naschie. The Fibonacci Code behind Super Strings and P-Branes: An Answer to M. Kakus Fundamental Question. Chaos, Solitons & Fractals. 31 (2007): 537–547.
M.S. El Naschie. Notes on Superstrings and the Infinite Sums of Fibonacci and Lucas Numbers. Chaos, Solitons & Fractals. 12 (2001): 1937–1940.
A.P. Stakhov. Fibonaccci Matrices: A Generalization of the Cassini Formula and a New Coding Theory. Chaos, Solitons Fractals. 30 (2006). 56–66.