Journal of Integer Sequences, Vol. 15 (2012), Article 12.8.2

Riordan-Bernstein Polynomials, Hankel Transforms and Somos Sequences

Paul Barry
School of Science
Waterford Institute of Technology


Using the language of Riordan arrays, we define a notion of generalized Bernstein polynomials which are defined as elements of certain Riordan arrays. We characterize the general elements of these arrays, and examine the Hankel transform of the row sums and the first columns of these arrays. We propose conditions under which these Hankel transforms possess the Somos-4 property. We use the generalized Bernstein polynomials to define generalized Bézier curves which can provide a visualization of the effect of the defining Riordan array.

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(Concerned with sequences A000007 A000045 A000108 A000984 A001006 A005773 A006318 A006720 A007318 A008288 A033184 A104562 .)

Received June 1 2012; revised version received September 23 2012. Published in Journal of Integer Sequences, October 2 2012.

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