A063001 - OEIS

%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