  This article is dedicated to the memory of Vadim Kuznetsov, and begins with
some of the author's recollections of him. Thereafter, a brief review of Somos
sequences is provided, with particular focus being made on the integrable
structure of Somos-4 recurrences, and on the Laurent property. Subsequently a
family of fourth-order recurrences that share the Laurent property are
considered, which are equivalent to Poisson maps in four dimensions. Two of
these maps turn out to be superintegrable, and their iteration furnishes
infinitely many solutions of some associated quartic Diophantine equations.
