[thijsr]

i was saying the in general we could assume that the rules changes with each entry, although for most puzzle they probably won't.
your rule for each entry (if taken to be constant), has a provision of the type: when n>18 the nth entry is 1. it is therefore of the type :
"if n>m then n=1" with m=18 outside of the initial data. for a mathematical sequence this is fine, not for a puzzle.

i'm sure we agree on most technical aspects of this matter.
i have to disagree though with the sense i was getting from your posts (maybe by mistake, in which case my apologies) that
'this type of thing makes no sense'.
that there is no mathematical rational why 'one solution is prefered above any other' is absolutely without any practical
meaning for a human being and as such an irrelevant critique to a puzzle.