All Questions

Are there any sequence given by a recurrence relation: $x_{n+t}=P(x_t,\cdots,x_{t+n-1})$, where $P$ is a positive Laurent Polynomial, satisfy: if $x_0=\cdots=x_{n-1}=1$, then the sequence is only ...

Let $\{s_n\}$ be the Somos-$4$ sequence, which is defined by $$s_{n+4}s_n=\alpha s_{n+3}s_{n+1}+\beta s_n^2.$$ It is known that $s_n$ is a Laurent polynomial: $s_n\in\mathbb{Z}[s_1^{\pm1}, \ldots, s_4^...

The terms of the sequence A276123, defined by $a_0=a_1=a_2=1$ and $$a_n=\dfrac{(a_{n-1}+1)(a_{n-2}+1)}{a_{n-3}}\;,$$ are all integers (it's easy to prove that for all $n\geq2$, $a_n=\frac{9-3(-1)^n}{2}...