Log-Convexity of some Recurrence Sequences

This paper focuses on the log-convexity of various combinatorial sequences. We mainly discuss several kinds of recurrence sequences, which include two three-term linear recurrence sequences, a nonlinear recurrence sequence, and two four-term linear recurrence sequences. We firstly give some new sufficient conditions for the log-convexity of these recurrence sequences and then, as applications, we show that a number of combinatorial sequences are log-convex.