Main Article Content
In this paper, we present linear summation formulas for generalized Pentanacci numbers and generalized Gaussian Pentanacci numbers. Also, as special cases, we give linear summation formulas of Pentanacci and Pentanacci-Lucas numbers; Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.
Natividad LR. On solving bonacci-like sequences of fourth, fth and sixth order. International Journal of Mathematics and Computing. 2013;3(2).
Rathore GPS, Sikhwal O, Choudhary R. Formula for nding nth term of bonacci-like sequence of higher order. International Journal of Mathematics and Its Applications. 2016;4(2-D):75-80.
Soykan Y. On generalized pentanacci and gaussian generalized pentanacci numbers. Preprints; 2019. 2019060110
Sloane NJA. The on-line encyclopedia of integer sequences.
Koshy T. Fibonacci and lucas numbers with applications. A Wiley-Interscience Publication, New York; 2001.
Koshy T. Pell and pell-lucas numbers with applications. Springer, New York; 2014. 1.
Gokbas H. Kose H. Some sum formulas for products of Pell and Pell-Lucas numbers. Int. J. Adv. Appl. Math. and Mech. 2017;4(4):1-4.
Parpar T. k'nc Mertebeden Rekurans Bagntsnn Ozellikleri ve Baz Uygulamalar, Selcuk Universitesi, Fen Bilimleri Enstitusu, Yuksek Lisans Tezi; 2011.
Soykan Y. Matrix sequences of tribonacci and tribonacci-lucas numbers; 2018
Waddill ME. The tetranacci sequence and generalizations. The Fibonacci Quarterly; 9.