Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.1

Riordan Pseudo-Involutions, Continued Fractions and Somos-4 Sequences

Paul Barry
School of Science
Waterford Institute of Technology


We define a three-parameter family of Bell pseudo-involutions in the Riordan group. The defining sequences have generating functions that are expressible as continued fractions. We indicate that the Hankel transforms of the defining sequences, and of the A sequences of the corresponding Riordan arrays, can be associated with a Somos-4 sequence. We give examples where these sequences can be associated with elliptic curves, and we exhibit instances where elliptic curves can give rise to associated Riordan pseudo-involutions. In the case of a particular one-parameter family of elliptic curves, we show how we can associate a unique Bell pseudo-involution with each such curve.

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(Concerned with sequences A000108 A000245 A004148 A006196 A006769 A007477 A023431 A025227 A025243 A025250 A025258 A025273 A050512 A060693 A068875 A086246 A089796 A090181 A091561 A091565 A105633 A130749 A152225 A178075 A178622 A178627 A187256 A217333.)

Received July 16 2018; revised versions received July 18 2018; June 27 2019. Published in Journal of Integer Sequences, August 24 2019.

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