On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

Abstract

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.

Generalized Fibonacci Numbers: Sum Formulas

“…Name of sequence Papers which deal with summing formulas Pell and Pell-Lucas [6], [7,8] Generalized Fibonacci [9,10,11,12,13] Generalized Tribonacci [14,15,16,17] Generalized Tetranacci [18,19,20] Generalized Pentanacci [21,22] Generalized Hexanacci [23] 2…”

On Summing Formulas for Horadam Numbers

“…Name of sequence Papers which deal with summing formulas Pell and Pell-Lucas [7], [8], [9] Generalized Fibonacci [10], [6] Generalized Tribonacci [11], [12], [13], [14] Generalized Tetranacci [15], [16], [17] Generalized Pentanacci [18], [19] Generalized Hexanacci [20] 2 SUMMING FORMULAS OF GENERALIZED FIBONACCI…”

On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers

“…Some summing formulas of the Pell and Pell-Lucas numbers are well known and given in [6], [7], see also [8]. For linear sums of Fibonacci, Tribonacci, Tetranacci, Pentanacci and Hexanacci numbers, see [9], [10], [11], [12], [13], and [14] respectively.…”