[seqfan] Hat puzzle related sequences?

[Christian Perfect]

Hi seqfans,
A friend is knitting a stripy hat, the sort which usually has the Fibonacci
sequence or the digits of pi encoded in it. She thought that was old hat
(ha) so she wanted to know if there are any sequences in the OEIS to do
with hat puzzles. A search for "hat" turned up http://oeis.org/A000983, but
nothing else.
Surely there must be more than one sequence relating to a hat puzzle in the
encyclopedia. Or are the solutions to the common hat puzzles all such
common sequences that they don't merit a note in their respective entries'
comment sections?