Elliptic curves and related sequences

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Sigma function solution of the initial value problem for Somos 5 sequences (2005, background): “Sequences that satisfy such fourth order recurrences are known as Somos 4 sequences [24, 29], and they originally arose in the theory of elliptic divisibility sequences [33, 34, 25].”
Recurrence Relations for Elliptic Sequences: Every Somos 4 is a Somos k (2004, methodology): “Christine Swart [11] has shown that the A(2)h ‘try to be’ the denominators of the x co-ordinates −eh = xM+hS , in that they succeed in so being at worst up to finitely many primes involved in the initial values and the defining recursion of the sequence (and thus in the coefficients of the model E o”
Elliptic Curves and Quadratic Recurrence Sequences (2005, methodology): “We note that in [28] the name ‘Somos 4’ is applied to all sequences defined over Q by a recurrence of form (1.”