One-parameter Darboux-deformed Fibonacci numbers

One-parameter Darboux deformations are established for the simple ordinary differential equation (ODE) satisfied by continuous generalizations of Fibonacci sequence recently discussed Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with Friedmann in FLRW homogeneous cosmology. The method allows introduction sequences, hence Darboux-deformed (noninteger) numbers. Considering same ODE as parametric oscillator equation, Ermakov–Lewis invariants these sequences also discussed.