Abstract
In this paper we investigate some basic properties of a general Tribonacci sequence, namely, a third order homogeneous anharmonic recurrence sequence, by way of the linesequential formalism developed previously for Fibonacci sequence, and report some new results. Some results are related or are reducible to known results as special cases. For consistency, we use the same nomenclatures, formats and conventions adopted in our previous works, see [3]–[5]. For publications in this area, see [1], [2], [9]–[14] and the references contained therein.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ando, S. “On a System of Sequences Defined by a Recurrence Relation.” The Fibonacci Quarterly, Vol. 33.3 (1995) : pp. 279–282.
Howard, F.T. “A Tribonacci Identity.” The Fibonacci Quarterly, Vol. 39.4 (2001): pp. 352–357.
Lee, Jack Y. “Some Basic Properties of the Fibonacci Line-sequence” , Applications of Fibonacci Numbers, Volume 4. Ed. G.E. Bergum, A.N. Philippou and A.F. Horadam. Dordrecht: Kluwer, 1990, pp. 203–214.
Lee, Jack Y. “The Golden-Fibonacci Equivalence.” The Fibonacci Quarterly, Vol. 30.3 (1992): pp. 216–220.
Lee, Jack Y. “Some Basic Translational Properties of the General Fiboancci Sequence”, Applications of Fibonacci Numbers, Volume 6. Ed. G.E. Bergum, A.N. Philippou and A.F. Horadam. Dordrecht: Kluwer, 1994, pp. 339–347.
Lee, Jack Y. “Some General Formulas Associated with the Second-Order Homogeneous Polynomial Line-Sequences.” The Fibonacci Quarterly, Vol. 39.5 (2001): pp. 419–429.
Lee, Jack Y. “On the Product of Line-Sequences.” The Fibonacci Quarterly, Vol. 40.5 (2002): pp. 438–440.
Liu, Bolian. “A Matrix Method to Solve Linear Recurrences with Constant Coefficients.” The Fibonacci Quarterly, Vol. 30.1 (1992) : pp. 2–8.
Scott, A., Delaney, T. and Hoggatt, V.E. Jr. “The Tribonacci Sequence.” The Fibonacci Quarterly, Vol. 15.3 (1977): pp. 193–201.
Spickerman, W.R. “Binet’s Formula for the aibonacci Seuqence.” The Fibonacci Quarterly, Vol. 20.2 (1982): pp. 118–120.
Waddill, M.E. “Using Matrix Techniques to Establish Properties of a Generalized Tribonacci Sequence” , Applications of Fibonacci Numbers, Volume 4. Ed. G.E. Bergum, A.N. Philippou and A.F. Horadam. Dordrecht: Kluwer, 1990, pp. 299–308.
Waddill, M.E. “The Tetranacci Sequence and Generalizations.” The Fibonacci Quarterly, Vol. 30.1 (1992): pp. 9–20.
Waddill, M.E. and Sacks, L. “Another Generalized Fibonacci Sequence.” The Fibonacci Quarterly, Vol. 5.3 (1967): pp. 209–222.
Yalavigi, C.C. “Properties of Tribonacci Numbers.” The Fibonacci Quarterly, Vol. 10.3 (1972): pp. 231–246.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Lee, J.Y. (2004). Some Basic Properties of a Tribonacci Line-Sequence. In: Howard, F.T. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-0-306-48517-6_15
Download citation
DOI: https://doi.org/10.1007/978-0-306-48517-6_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6545-2
Online ISBN: 978-0-306-48517-6
eBook Packages: Springer Book Archive