A Note on Sum Formulae of Generalized Pentanacci Sequence

During this paper, we first demonstrate the closed forms of sum formulae both \(\sum^\eta_{\lambda=0}\lambda z^\lambda A_\lambda\) and \(\sum^\eta_{\lambda=1}\lambda z^\lambda A_{-\lambda}\) for the generalized Pentanacci numbers. Then, we grant summation formulae for the sequences such as Pentanacci, Pentanacci-Lucas and other fifth-order iteration sequences.