On the binomial interpolated triangles

TL;DR

This paper explores a Pascal-like triangle transformed by the binomial interpolated transform, analyzing its properties, sums, and special classes, especially focusing on binary recurrences.

Contribution

It introduces a novel application of the binomial interpolated transform to Pascal-like triangles and characterizes their sums and special classes.

Findings

Derived sums of elements in rows and diagonals.

Defined two special classes of these arithmetical triangles.

Analyzed the transform's effect on binary recurrences.

Abstract

The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing on binary recurrences. We give the sums of the elements in rows and in rising diagonals, further we define two special classes of these arithmetical triangles.