2022/11/22 by Barry, Paul
#11A55 #15A15 #15B05 #15B36 #Combinatorics (math.CO) #FOS: Mathematics #Primary 11B37 #Secondary 05A15
paper · doi:10.48550/arxiv.2211.12637
We give conjectures on the form of families of integer sequences whose Hankel transforms are, respectively, (α, β) Somos 4 sequences, (α, 0, γ) Somos 6 sequences, and (α, β, γ, δ) Somos 8 sequences, for particular values of α, β, γ, δ which we describe. The sequences involved can be described in terms of the application of certain stretched Riordan arrays to the Catalan numbers, accompanied by a (sequence) Hankel transform. The combination of Riordan array and the Catalan numbers results from the study of certain generalized Jacobi continued fractions, based on the Counting Automata Methodology.