24 citations · 74 across the 56 of their papers we have counts for
59 papers
Square roots in the Appell group and Sprugnoli arrays
Paul Barry
We introduce a special mapping from pairs of power series to the group of Sprugnoli matrices. This mapping has the property when the second argument is an even power series, then t…
Pascal-like Sprugnoli arrays
Paul Barry
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 c…
A new group in the Riordan family of matrix groups: the Sprugnoli group
Paul Barry
We define a group of lower-triangular matrices whose columns are defined by power series. This group can be seen as a generalization of the (ordinary) Riordan group and the double…
Moment sequences, transformations, and Spidernet graphs
Paul Barry
We use the link between Jacobi continued fractions and the generating functions of certain moment sequences to study some simple transformations on them. In particular, we define a…
Integer sequences from elliptic curves
Paul Barry
We indicate that given an integer coordinate point on an elliptic curve y^2+axy+by=x^3+cx^2+dx+e we can identify an integer sequence whose Hankel transform is a Somos-4 sequence, a…
Conjectures on Somos , and sequences using Riordan arrays and the Catalan numbers
Paul Barry
We give conjectures on the form of families of integer sequences whose Hankel transforms are, respectively, Somos sequences, Somos sequences, and $(α,…