Transactions of the American Mathematical Society

Author(s): A. N. W. Hone
Journal: Trans. Amer. Math. Soc. 359 (2007), 5019-5034.
MSC (2000): Primary 11B37, 33E05; Secondary 37J35
Posted: April 24, 2007
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Abstract: The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.

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