PreprintCC BY 4.0arXiv
Pascal-like Sprugnoli arrays
Abstract
In this note, we look at the structure and properties of palindromic or Pascal-like Sprugnoli arrays. We show that there are two closely related families of these arrays. We give closed form expressions for the elements of these families, and in each case, we describe the form of the inverse arrays. Finally, we consider the arrays modulo $2$ and the resulting arithmetic sequences.
Related
- Orthogonal polynomials on two or more intervals: the Sprugnoli context
- A new group in the Riordan family of matrix groups: the Sprugnoli group
- A New Group in the Riordan Family of Matrix Groups: the Sprugnoli Group
- Pascal tiling and congruences modulo N in Pascal's triangle
- A cohomological equation related to the Pascal transformation
BibTeX
@misc{barry2026pascallike,
title = {{Pascal-like Sprugnoli arrays}},
author = {Paul Barry},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.22070},
eprint = {2606.22070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.22070},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pascal-like Sprugnoli arrays
AU - Paul Barry
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2606.22070
UR - https://arxiv.org/abs/2606.22070
AB - In this note, we look at the structure and properties of palindromic or Pascal-like Sprugnoli arrays. We show that there are two closely related families of these arrays. We give closed form expressions for the elements of these families, and in each case, we describe the form of the inverse arrays. Finally, we consider the arrays modulo $2$ and the resulting arithmetic sequences.
ER -