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. Consi...

Fibonacci cubes, extended Fibonacci cubes, and Lucas cubes are induced subgraphs of hypercubes 9 defined in terms of Fibonacci strings. It is shown that all these graphs are median. Several enumeration results on the number of their edges and squares are obtained. Some identities involving Fibonacci 11 and Lucas numbers are also presented. © 2005 Published by Elsevier B.V. 13

Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with help generating functions their functional equations. In this paper, we define generalized (p,q)-Bernoulli–Fibonacci (p,q)-Bernoulli–Lucas polynomials numbers by using (p,q)-Bernoulli numbers, unified h(x)-Fibonacci h(x)-Lucas polynomials. We als...