On the Reciprocal Sums and Products of mth-order Linear Recursive Sequences
Tingting Du
Research Center for Number Theory and Its Application
Northwest University
Xi'an, Shaanxi 710127
China
Abstract:
The mth-order linear recursive sequence of
(wn)n ≥ 0
is defined by the recursion wn
= a1wn−1 +
a2wn−2 + ... +
amwn−m for
n > m. In previous discussions of the reciprocal sums
and products of (wn)n ≥
0, the condition a1 ≥ a2 ≥
... ≥ am ≥ 1 was typically imposed. In
this paper, we extend previous research and allow the coefficients to
be arbitrary positive integers.
Full version: pdf,
dvi,
ps,
latex
Received October 25 2023; revised versions received October 27 2023; January 11 2024; January 17 2024.
Published in Journal of Integer Sequences,
January 17 2024.
Return to
Journal of Integer Sequences home page
