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%I #7 May 25 2021 02:37:23
%S 5,24,109,435,1512,4621,12463,29565,60596,104542,147032,161759,130777,
%T 68989,17681
%N Number of paths of length n+2 originating at a non-corner edge of 4 X 4 Boggle board.
%C A legal walk on a Boggle board is from one vertex to a vertex adjacent orthogonally or diagonally.
%H Eugene McDonnell, <a href="/A063000/a063000.txt">Remarks on Game of "Boggle"</a>
%F Formula unknown, values computed empirically.
%o (Python)
%o def nn(c): # neighbors of c
%o i, j = divmod(c, 4)
%o N = set((i+io, j+jo) for io in [-1, 0, 1] for jo in [-1, 0, 1]) - {(i, j)}
%o return [4*i+j for i, j in N if 0 <= i < 4 and 0 <= j < 4]
%o def afind():
%o n, paths = 0, {(1, )}
%o while n+2 <= 16:
%o paths1 = set(p + (e, ) for p in paths for e in nn(p[-1]) if e not in p)
%o print(len(paths1), end=", ")
%o n, paths = n+1, paths1
%o afind() # _Michael S. Branicky_, May 24 2021
%Y Cf. A063000, A063002.
%K fini,full,nonn
%O 0,1
%A Eugene McDonnell (EEMcD(AT)AOL.com), Jul 01 2001
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