### Gaussian Tetranacci Numbers

#### Abstract

In this paper, we define Gaussian Tetranacci sequence. Moreover, we give generating function, Binet-like formula, sum formulas and matrix representation of Gaussian tetranacci numbers.

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PDF#### References

M. Feinberg. “Fibonacci-Tribonacci.” Fibonacci Quarterly 1. 3 (1963):71-74.

W. R. Spickerman & R. N. Joyner. "Binet’s Formula for the Recursive Sequence of Order K." Fibonacci Quarterly 22.4 (1984):327-31.

T. B. Kirkpatrick, Jr. "Fibonacci Sequences and Additive Triangles of Higher Order and Degree." Fibonacci Quarterly 15. 4 (1977):319-22.

W. I. McLaughlin. "Note on a Tetranacci Alternative to Bode’s Law." Fibonacci Quarterly 17. 2 (1979):116-17.

R. Scheon. "Harmonic, Geometric and Arithmetic Means in Generalized Fibonacci Sequences." Fibonacci Quarterly 22. 4 (1984):354-57.

J. Arkin, D. C. Arney, G. E. Bergum, S. A. Burr, & B. J. Porter. "Unique Fibonacci Formulas." Fibonacci Quarterly 27. 4 (1989):296-302.

M. E. Waddill. “The Tetranacci Sequence and Generalizations.” The Fibonacci Quarterly, 30.1 (1992) 9.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

E. Gurel. “k-order Gaussian Fibonacci and k-order Gaussian Lucas Recurrence Relations”. Ph.D Thesis. Pamukkale University Institute of Science Mathematics. Denizli, Turkey. (2015).

G. Berzsenyi. “Gaussian Fibonacci numbers”, The Fibonacci Quarterly, 15 (3): 233-236 (1977).

C. J. Harman. “Complex Fibonacci numbers”, The Fibonacci Quarterly, 19 (1): 82-86 (1981).

S. Pethe, & A. F. Horadam. “Generalized Gaussian Fibonacci Numbers”, Bull. Austral. Math. Soc., 33: 37-48 (1986).

J. H. Jordan. “Gaussian Fibonacci and Lucas Numbers”, The Fibonacci Quarterly, 3 (4): 315-318 (1965).

A. F. Horadam. “Complex Fibonacci Numbers and Fibonacci Quaternions”, Amer. Math. Monthly, 70: 289-291 (1963).

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