A Study On Generalized (r,s,t,u,v,y)-Numbers
Keywords:
Hexanacci numbers,, (r,s,t,u,v,y) numbers,, Lucas (r,s,t,u,v,y) numbers,, modified (r,s,t,u,v,y) numbers.
Abstract
In this paper, we introduce the generalized (r,s,t,u,v,y) sequence and we deal with, in detail, three special cases which we call them (r,s,t,u,v,y), Lucas (r,s,t,u,v,y) and modified (r,s,t,u,v,y) sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.
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References
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Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 2013.
Rathore, G.P.S., Sikhwal, O., Choudhary, R., Formula for finding nth Term of Fibonacci-Like Sequence of Higher Order, International Journal of Mathematics And its Applications, 4 (2-D), 75-80, 2016.
Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/
Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.
Soykan Y, Özmen, N., On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers, Submitted.
Soykan, Y., On Generalized Sixth-Order Pell Sequence, Journal of Scientific Perspectives, 4(1), 49-70, 2020, DOİ: https://doi.org/10.26900/jsp.4.005.
Soykan, Y., Properties of Generalized 6-primes Numbers, Archives of Current Research International, 20(6), 12-30, 2020. DOI: 10.9734/ACRI/2020/v20i630199
Stanley, R. P., Generating Functions, Studies in Combinatorics, MAA Studies in Mathematics, Math. Assoc. of America, Washington, D.C., 17, 100-141, 1978.
Published
2020-11-27
How to Cite
Soykan, Y. (2020). A Study On Generalized (r,s,t,u,v,y)-Numbers. Journal of Progressive Research in Mathematics, 17(1), 54-72. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1951
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