Some number arrays related to Pascal and Lucas triangles
Journal
Journal of Integer Sequences
ISSN
1530-7638
Date Issued
2013-06
Author(s)
Pita-Ruiz, Claudio
Type
text::journal::journal article
Abstract
By taking repeated convolutions of the sequence n
p with the constant sequence 1,
we form the number arrays of the coefficients resulting when we write the mentioned
convolutions as linear combinations of certain binomial coefficients. According to this
procedure, Pascal and Lucas triangles correspond to the cases p = 1 and p = 2 respectively. We show that these arrays have some properties similar to the well-known
properties of Pascal and Lucas triangles.
p with the constant sequence 1,
we form the number arrays of the coefficients resulting when we write the mentioned
convolutions as linear combinations of certain binomial coefficients. According to this
procedure, Pascal and Lucas triangles correspond to the cases p = 1 and p = 2 respectively. We show that these arrays have some properties similar to the well-known
properties of Pascal and Lucas triangles.