Preprint Article Version 1 This version is not peer-reviewed

# On Generalized Tetranacci Numbers: Closed Form Formulas of the Sum $\sum_{k=0}^{n}W_{k}^{2}$ of the Squares of Terms

Version 1 : Received: 26 May 2020 / Approved: 27 May 2020 / Online: 27 May 2020 (12:28:48 CEST)

How to cite: Soykan, Y. On Generalized Tetranacci Numbers: Closed Form Formulas of the Sum $\sum_{k=0}^{n}W_{k}^{2}$ of the Squares of Terms. Preprints 2020, 2020050453 (doi: 10.20944/preprints202005.0453.v1). Soykan, Y. On Generalized Tetranacci Numbers: Closed Form Formulas of the Sum $\sum_{k=0}^{n}W_{k}^{2}$ of the Squares of Terms. Preprints 2020, 2020050453 (doi: 10.20944/preprints202005.0453.v1).

## Abstract

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}W_{k}^{2}$ \ for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas $\sum_{k=0}^{n}W_{k+1}W_{k},$ $\sum_{k=0}^{n}W_{k+2}W_{k},$ and $\sum_{k=0}^{n}W_{k+3}W_{k}.$ As special cases, we give summation formulas of the of Tetranacci, Tetranacci-Lucas and some other fourth order linear recurrance sequences.

11B39; 11B83