A simplified Binet formula for k-generalized Fibonacci numbers

Details A simplified Binet formula for k-generalized Fibonacci numbers A simplified Binet formula for k-generalized Fibonacci numbers

2009-05-04

arxiv.org/abs/0905.0304v2

Mathematics

Number Theory

8 pages, bibliography

Scientific paper

We present a particularly nice 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 to generate the desired sequence. These results were also found (independently) at about the same time by Zhaohui Du of Singapore, China. We are working on a joint paper.

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