On the Fibonacci k-numbers

@article{Falcn2007OnTF,
  title={On the Fibonacci k-numbers},
  author={S. Falc{\'o}n and Angel Plaza},
  journal={Chaos Solitons & Fractals},
  year={2007},
  volume={32},
  pages={1615-1624}
}
We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {Fk,n}n=0∞ were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers are deduce directly from elementary matrix algebra. 
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References

SHOWING 1-10 OF 43 REFERENCES
Theory of Binet formulas for Fibonacci and Lucas p-numbers
  • 96
  • PDF
The Fibonacci Numbers—Exposed
  • 101
  • PDF
The Fibonacci Numbers—Exposed More Discretely
  • 55
  • PDF
The continuous functions for the Fibonacci and Lucas p-numbers
  • 39
Fibonacci and Lucas Numbers
  • 251
  • PDF
The Golden Shofar
  • 55
  • PDF
...
1
2
3
4
5
...