Pell and associated Pell braid sequences as GCDs of sums of $k$ consecutive Pell, balancing, and related numbers

aBa Mbirika, Janee Schrader, Jürgen Spilker

We consider the greatest common divisor (GCD) of all sums of $k$ consecutive terms of a sequence $(S_n{)}_{n\ge 0}$ where the terms $S_n$ come from exactly one of following six well…