Somos Sequence
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High Quality Content by WIKIPEDIA articles! A Somos-k sequence, for an integer number k, is defined by the equation a_n a_{n-k} = a_{n-1} a_{n-k+1} + a_{n-2} a_{n-k+2} + cdots + a_{(n+1)/2} a_{(n-1)/2} when k is odd, or by the analogous equation a_n a_{n-k} = a_{n-1} a_{n-k+1} + a_{n-2} a_{n-k+2} + cdots + a_{n/2}^2 when k is even. For instance, for the first nontrivial case, k = 4, the defining equation is a_n a_{n-4} = a_{n-1} a_{n-3} + a_{n-2}^2 while for k = 5 the equation is a_n a_{n-5} = a_{n-1} a_{n-4} + a_{n-2} a_{n-3},.

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High Quality Content by WIKIPEDIA articles! A Somos-k sequence, for an integer number k, is defined by the equation a_n a_{n-k} = a_{n-1} a_{n-k+1} + a_{n-2} a_{n-k+2} + cdots + a_{(n+1)/2} a_{(n-1)/2} when k is odd, or by the analogous equation a_n a_{n-k} = a_{n-1} a_{n-k+1} + a_{n-2} a_{n-k+2} + cdots + a_{n/2}^2 when k is even. For instance, for the first nontrivial case, k = 4, the defining equation is a_n a_{n-4} = a_{n-1} a_{n-3} + a_{n-2}^2 while for k = 5 the equation is a_n a_{n-5} = a_{n-1} a_{n-4} + a_{n-2} a_{n-3},.