Let Tn = Tn(k) be the generalized Fibonacci sequence of order k defined by the recurrence Tn = Tn1 + Tn2 + · · · + Tnk, n k, with T0 = 0 and T1 = T2 = · · · = Tk1 = 1. In this paper, we fully and partially characterize the 2-adic valuations of Tn(4) and Tn(5), respectively. Moreover, we provide new addition formulas and congruences for the sequences {Tn(k)}n0.
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