Summing Formulas For Generalized Tribonacci Numbers
Y\"uksel Soykan
TL;DR
This paper derives closed-form summation formulas for generalized Tribonacci numbers and related third-order recurrence sequences, unifying and extending previous results with new formulas for various special cases.
Contribution
It provides new closed-form summation formulas for generalized Tribonacci numbers and related sequences, including some that were not previously known.
Findings
Closed-form summation formulas for generalized Tribonacci numbers.
Recovery of previous results as special cases.
New formulas for sequences like Pell-Padovan and Padovan-Perrin.
Abstract
In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third order linear recurrance sequences. All the summing formulas of well known recurrence sequences which we deal with are linear except the cases Pell-Padovan and Padovan-Perrin.
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