Linear Recurrence Sequences and Their Convolutions via Bell Polynomials
Department of Mathematics
Rochester, NY 14618
Juan B. Gil and Michael D. Weiner
Department of Mathematics and Statistics
Penn State Altoona
Altoona, PA 16601
We recast homogeneous linear recurrence sequences with fixed
coefficients in terms of partial Bell polynomials, and use their
properties to obtain various combinatorial identities and multifold
convolution formulas. Our approach relies on a basis of sequences that
can be obtained as the INVERT transform of the coefficients of the
given recurrence relation. For such a basis sequence with generating
and for any positive integer r, we give a formula
for the convolved sequence generated by
Y(t)r and prove that it
satisfies an elegant recurrence relation.
Full version: pdf,
(Concerned with sequences
May 29 2014;
revised versions received November 28 2014; November 29 2014.
Published in Journal of Integer Sequences, December 14 2014.
Journal of Integer Sequences home page