TY - JOUR
AU - Helmut Prodinger
PY - 2020/12/14
Y2 - 2024/10/11
TI - Summing a family of generalized Pell numbers
JF - Annales Mathematicae Silesianae
JA - AMSil
VL - 35
IS - 1
SE -
DO -
UR - https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13477
AB - A new family of generalized Pell numbers was recently introduced and studied by BrĂ³d ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power Pnl is expressed as a linear combination of Pmn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R=2r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.
ER -