[seqfan] Knights-move Ulam-Warburton - nice problem

[Neil Sloane]

Dear Seq Fans, Someone who watched the Terrific Toothpicks Numberphile
video on Youtube suggested a knights-move version.  I looked this up in the
OEIS of course and found that Remy Sigrist had already studied it. The
illustrations (excluding mine) are lovely, and so is the problem.
The original sequences are A319018, A319019; while trying to analyze it I
added three more last night, A322048, -049, -050.

The main problem to crack is what is A322049.(which gives the growth from
the corners of the octagon after a power of 2 generations)?

It would be nice to have a really big b-file (or a-file or both) for
A322050.

Another question: look at the rows of the triangle in A322050. They are
converging to the sequence A322049. The number of terms in rows 1,2,3,4,...
that agree with the limit are 1,1,2,4,7,11,22 (I think). How does this
continue? This is not yet in the OEIS.