Given a fixed positive integer $n \geq 3$, I want to generate a list of lists in gap with the following properties:
each list has $n$ entries $a\_0,a\_1,\ldots,a\_{n-1}$. We have:

* $\min(a\_0,a\_1,\ldots,a\_{n-1})=a\_0 \geq2$
* $a\_0 \leq n+1$
* $a\_{n-1}=a\_0+1$ and 
$a\_i -1 \leq a\_{i+1}$ for $i=0,\ldots,n-2$.
What is the easiest way to do this in gap?

edit: I modified the above conditions a little because its enough to look at a little smaller class of such lists.(in fact $a\_0 \leq n+1$ implies that the maximum of all $a\_i$ has a good bound)

here is an example for n=6 :

```
L:=Cartesian([2,3,4,5,6,7],[2,3,4,5,6,7,8,9,10,11,12],
[2,3,4,5,6,7,8,9,10,11,12],[2,3,4,5,6,7,8,9,10,11,12],
[2,3,4,5,6,7,8,9,10,11,12],[3,4,5,6,7,8]);

LL:=Filtered(L, x->Minimum(x)>=2 and 
                x[6]=x[1]+1 and 
                Minimum(x)=x[1] and 
                x[2]-1 <=x[3] and 
                x[3]-1<=x[4] and 
                x[4]-1<=x[5] and 
                x[5]-1<=x[6]);

```

Using Cartesian, gap in combination with my computer isn't able to do this even for n=8.

By the way the motivation behind this is that those lists parametrise nonselfinjective Nakayama algebras with certain Kupisch series of theoretical interest.
here is the number of such lists: <https://oeis.org/A007946>

it doesn't grow that much, so how can i avoid generating large lists and then have to filter?