The 2-adic and 3-adic valuation of the Tripell sequence and an application

Abstract

Let (Tn)n≥0 denote the Tripell sequence, defined by the linear recurrence Tn = 2Tn−1 + Tn−2 + Tn−3 forn ≥ 3 with T0 = 0, T1 = 1 and T2 = 2 as initial conditions. In this paper, we study the 2-adic and 3-adic valuation ofthe Tripell sequence and, as an application, we determine all Tripell numbers which are factorials.