Linear recurrence sequences with indices in arithmetic progression and their sums
Number Theory
2016-11-29 v2
Abstract
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given explicitly in terms of partial Bell polynomials that depend on at most d-1 terms of the generalized Lucas sequence associated with the given recurrence. We also provide an elegant formula for the partial sums of such sequences and illustrate all of our results with examples of various orders, including common generalizations of the Fibonacci numbers.
Cite
@article{arxiv.1505.06339,
title = {Linear recurrence sequences with indices in arithmetic progression and their sums},
author = {Daniel Birmajer and Juan B. Gil and Michael D. Weiner},
journal= {arXiv preprint arXiv:1505.06339},
year = {2016}
}
Comments
11 pages. In this version we fixed a minor mistake and reorganized the paper to better display our main result