Summation Formulas for Generalized Tetranacci Numbers

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Yüksel Soykan


In this paper, closed forms of the summation formulas for generalized Tetranacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, fourth order Pell, fourth order Pell-Lucas, fourth order Jacobsthal, fourth order Jacobsthal-Lucas numbers.

Tetranacci numbers, Tetranacci-Lucas numbers, sum formulas, summing formulas.

Article Details

How to Cite
Soykan, Y. (2019). Summation Formulas for Generalized Tetranacci Numbers. Asian Journal of Advanced Research and Reports, 7(2), 1-12.
Original Research Article


Hathiwala GS, Shah DV. Binet–type formula for the sequence of Tetranacci numbers by alternate methods. Mathematical Journal of Interdisciplinary Sciences. 2017;6(1):37-48.

Melham RS. Some analogs of the identity F2n + F2 n+1 = F2 2n+1. Fibonacci Quarterly. 1999;305-311.

Natividad LR. On solving fibonacci-like sequences of fourth, fifth and sixth order. International Journal of Mathematics and Computing. 2013;3(2).

Singh B, Bhadouria P, Sikhwal O, Sisodiya K. A formula for Tetranacci-like sequence. Gen. Math. Notes. 2014;20(2):136-141.

Waddill ME. The Tetranacci sequence and generalizations. Fibonacci Quarterly. 1992;9-20.

Waddill. Another generalized Fibonacci sequence. M. E., Fibonacci Quarterly. 1967;5(3):209-227.

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.

G¨okbas¸ H, K¨ose, H. Some sum formulas for products of Pell and Pell-Lucas numbers. Int. J. Adv. Appl. Math. and Mech. 2017;4(4):1-4.

Hansen RT. General identities for linear Fibonacci and Lucas summations. Fibonacci Quarterly. 1978;16(2):121-28.

Soykan Y. On summing formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers. Advances in Research. 2019;20(2):1-15.

Frontczak R. Sums of Tribonacci and Tribonacci-Lucas numbers. International Journal of Mathematical Analysis. 2018;12(1):19-24.

Parpar T. K’ncı Mertebeden Rek¨ urans Bag˘ ıntısının O¨ zellikleri ve Bazı Uygulamaları, Selc¸uk U¨ niversitesi, Fen Bilimleri Enstit ¨us¨ u, Y¨uksek Lisans Tezi; 2011.

Soykan Y. Summing formulas for generalized Tribonacci numbers. arXiv:1910.03490v1 [math.GM]; 2019.

Soykan Y. Matrix sequences of Tribonacci and Tribonacci-Lucas numbers. arXiv:1809.07809v1 [math.NT] 20 Sep 2018.

Soykan Y. Linear summing formulas of generalized Pentanacci and gaussian generalized Pentanacci numbers. Journal of Advanced in Mathematics and Computer Science. 2019;33(3):1-14.

Soykan Y. On summing formulas of generalized Hexanacci and Gaussian Generalized Hexanacci numbers. Asian Research Journal of Mathematics. 2019;14(4):1-14. Article no.ARJOM.50727.

Sloane NJA. The on-line encyclopedia of integer sequences. Available: