What's really neat about this problem is that the 3D example, a bird in a cage, was solved sooner and is much simpler

I feel like the answer should be much simpler than that equation salad.

In computer science, you steal the box from the psych department and put children in it so you can sell them loot crates

Also zoology

This should do it, or am I missing something?

I'm just nodding along and hoping no one notices i don't know what's happening

Unless your snake is an ouroboros, I don't think folks will count the head and tail as consecutive

10?

Some lower bounds have been established: https://oeis.org/A099155

I'd think that it's not "too much to be brute forced", but probably no one has thrown enough resources at that recently

Some trivial bounds: F(n-1) + 1 <= F(n) <= F(n-1) * 2 + 1.

Also F(n) <= 2^(n-1)

More of a "This is how we weigh a critter that won't stay put for more than .3 seconds"

Took me a while to follow that too! The three examples of fails at the top each show instances where there are non-consecutive parts of the snake on adjacent corners - it's the lines highlighted in red.

Basically no two parts of the snake that aren't directly joined to each other in the snake are allowed to be on corners which are only a line apart.

I think.

Any two coils that are not directly connected. For example, suppose we number from the head, coil 1, 2, 3, 4. Then pairs that are not directly connected are: (1, 3), (1, 4), (2, 4). The endpoints of these pairs of segments cannot be connected by an edge of the cube.