[seqfan] Re: Knights-move Ulam-Warburton - nice problem
bradklee at gmail.com
Mon Dec 17 17:32:59 CET 2018
If you break A322049 to an irregular triangle so that rows start with n = 2^k,
then another two limit sequences will appear from buried under about two
layers of disorder:
L1: 8, 49, 33, 165, 46, 270, 91, 436, 55, 300, 157, 781, 149, 787 . . .
L2: 8, 45, 34, 166, 49, 273, 91, 435, 57, 303, 157, 774, 151, 790 . . .
Sequences L1 and L2 are negligibly different, alternate between even/odd k,
and look resilient to functional analysis (even allowing for recursion).
Another set of probably easier questions involves characterization of the
underlying fractal geometry. Toward that end, I've added a comment to
A319018 and a new picture with log-periodic coloring :
> > https://oeis.org/A322050/a322050_1.png
I didn't see any notes--is the identity A322050(2^k+1)=1 proven, or only
an assertion thus far? Proving the fractal structure could be a nice first
step leading into a comparison with aperiodic substitution tilings.
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