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.