Answer by Alexey Ustinov for Does this sequence always give an integer?
Andrew Hone in the articles Analytic solutions and integrability for bilinear recurrences of order six and Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties...
View ArticleAnswer by Alexey Ustinov for Does this sequence always give an integer?
It is not an answer just a piece of fun. I've made a mistake in my program and calculated the sequence with wrong recurrence $$a_{n+6}=\frac{a_{n+5}\cdot a_{n+1}+a_{n+4}\cdot a_{n+2}\cdot...
View ArticleAnswer by David E Speyer for Does this sequence always give an integer?
This is the special case $(p,q,r)=(1,2,3)$ of the $3$-term Gale-Robinson recurrence:$$x_{n+p+q+r} x_n = x_{n+p} x_{n+q+r} + x_{n+q} x_{n+p+r} + x_{n+p+q} x_{n+r}$$Fomin and Zelevinsky proved that,...
View ArticleAnswer by M. Khan for Does this sequence always give an integer?
The following article by Ekhad and Zeilberger might be of interest.http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/somos.html
View ArticleDoes this sequence always give an integer?
It is known that the $k$-Somos sequences always give integers for $2\le k\le 7$.For example, the $6$-Somos sequence is defined as the following : $$a_{n+6}=\frac{a_{n+5}\cdot a_{n+1}+a_{n+4}\cdot...
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