A Note on Sum Formulae of Generalized Pentanacci Sequence
Yuksel Soykan
Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
Erkan Tasdemir *
Pinarhisar Vocational School, Kirklareli University, 39300, Kirklareli, Turkey.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Pentanacci numbers, pentanacci-lucas numbers, sum formulae, summing formulae