On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

In this paper, we present linear summation formulas for generalized Hexanacci numbers and generalized Gaussian Hexanacci numbers. Also, as special cases, we give linear summation formulas of Hexanacci and Hexanacci-Lucas numbers; Gaussian Hexanacci and Gaussian Hexanacci-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. In fact, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.