Here's a very short sequence of integers that isn't in the #OEIS yet:
2, 3, 5, 6, 7, 10, 11.
(we can have a debate about whether 1 should be in the list)
As usual, I'll give you this sequence without any context, and you can try to work out what it represents, if you like. I'll reply to this post with a diagram that explains where it came from, under the content warning "massive spoiler diagram".
A colleague had their first baby recently, so we've got the baby presents and thought about what you write in a "new baby" card.
When one of mine was born, @peterrowlett gave me the invaluable gift of a card with the words to a lullaby in it, so I'm passing on my own lullaby, which appeals to me because it's just an integer sequence and I can recreate it from first principles: https://aperiodical.com/2021/07/a-lullaby-sequence/
You have pieces labelled 1 to N.
You arrange them in a line N times, so that at turn k the piece labelled k is in position k. (so on the first turn piece 1 is at the start, on turn 2 piece 2 is next to that, and so on)
No piece can be in the same position for two consecutive turns.
How many ways of doing this are there?
For N=3, there's only one:
On turn 1, it must be 1xx
On turn 2, it must be x2x and 2 can't be where it was before, so turn 1 was 132 and turn 2 is 321.
On turn 3 it must be 213.