Tribonacci Sequences With Certain Indices and Their Sums

Abstract

In this paper, we derive new recurrence relations and generating matrices for the sums of usual Tribonacci numbers and $4n$ subscripted Tribonacci sequences, $\{T_{4n}\}$, and their sums. We obtain explicit formulas and combinatorial representations for the sums of terms of these sequences. Finally, we represent relationships between these sequences and permanents of certain matrices.