Generalized Heisenberg algebras andk-generalized Fibonacci numbers

It is shown how some of the recent results of de Souza et al ( 2006 J. Phys. A: Math. Gen. 39 10415 ) can be generalized to describe Hamiltonians whose eigenvalues are given as k -generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al correspond to k = 2.