On the Smarandache-Pascal derived sequences of generalized Tribonacci numbers

For any sequence recurrence formula, the Smarandache-Pascal derived sequence { T n } of { b n } is defined by T n + 1 = ∑ k = 0 n ( n k ) ⋅ b k + 1 for all n ≥ 2 , where ( n k ) = n ! k ! ( n − k ) ! denotes the combination number. The recurrence formula of { T n } is obtained by the properties of the third-order linear recurrence sequence.