Generalized Tribonacci Sequence and its Sum Through Third Order Difference Operator

This study presents the generalized third-order difference operator with constant coefficients and inverse, allowing us to construct a sequence similar to the generalized k-Fibonacci sequence. We refer to this sequence as the generalized Tribonacci sequence and prove certain lemmas and theorems regarding its generalized Tribonacci sums. We have included relevant examples validated using MATLAB to demonstrate our primary findings better.AMS Subject classification: 11B37, 11B39, 11B83, 39A70.