$C_{\lambda}$-extended harmonic oscillator and (para)supersymmetric   quantum mechanics
  $C_{\lambda}$-extended oscillator algebras are realized as generalized deformed oscillator algebras. For $\lambda = 3$, the spectrum of the corresponding bosonic oscillator Hamiltonian is shown to strongly depend on the algebra parameters. A connection with cyclic shape invariant potentials is noted. A bosonization of PSSQM of order two is obtained. 
C. Quesne, N. Vansteenkiste