Abstract
In this note, we present two sufficient conditions for determining the signs of three-term recurrence sequences. In order to determine the signs of some sequences, by our method, it suffices to compute a constant number of terms at the beginning. For example, in order to prove the positivity of the central Delannoy number D ( n ) , by our method, it just needs to know the recurrence relation of D ( n ) and the values of D ( k ) for 0 ≤ k ≤ 2 . As applications, we determine the signs of some famous sequences.
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