Category talk:Somos-4 sequence

Bilinear or quadratic?

Somos-4 sequence: bilinear recurrence of order 4 of the form

$a_{n+2}\ a_{n-2}=\alpha \ a_{n+1}\ a_{n-1}+\beta \ {a_{n}}^{2},\,$ or equivalently $a_{n+2}={\frac {\alpha \ a_{n+1}\ a_{n-1}+\beta \ {a_{n}}^{2}}{a_{n-2}}}\,$

A function of two variables is bilinear if it is linear with respect to each of its variables. (Cf. Weisstein, Eric W., Bilinear Function, from MathWorld—A Wolfram Web Resource.)

Harry W. Braden, Victor Z. Enolskii, Andrew N.W. Hone, Bilinear recurrences and addition formulae for hyperelliptic sigma functions, arXiv (2005.)

It seems to me that it should be considered a quadratic sequence since it is quadratic in $\scriptstyle a_{n}\,$, although in the above mentioned arXiv paper it is considered multilinear (Why? I am confused here...) — Daniel Forgues 23:42, 17 October 2010 (UTC)