Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant

@article{Faraoni2021GeneralizedFN,
  title={Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant},
  author={Valerio Faraoni and Farah Atieh},
  journal={Symmetry},
  year={2021},
  volume={13},
  pages={200}
}
Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing a spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence. 
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