The Log-Behavior of the Partial Sum for the Tribonacci Numbers

Let {T_n}_n ≥ 0 and {T_n^[1]}_n ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {T_n}_n ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of T_n^[1]}_n ≥ 1 and the log-balancedness of some sequences involving T_n^[1]. In addition, we discuss the monotonicity of some sequences related to T_n^[1].