Journal of Integer Sequences, Vol. 17 (2014), Article 14.4.7

A Simplified Binet Formula for k-Generalized Fibonacci Numbers

Gregory P. B. Dresden
Department of Mathematics
Washington and Lee University
Lexington, VA 24450

Zhaohui Du


In this paper, we present a Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc.). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula in order to generate the desired sequence.

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(Concerned with sequences A000073 A000078 A001591.)

Received October 15 2008; revised versions received February 19 2014; February 23 2014. Published in Journal of Integer Sequences, February 26 2014.

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