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A063000
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Number of paths of length n+2 originating at a corner of a 4 X 4 Boggle board.
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3
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3, 15, 75, 322, 1184, 3814, 10918, 27772, 61734, 116966, 183256, 228016, 211502, 128994, 37948
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OFFSET
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0,1
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COMMENTS
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A legal walk on a Boggle board is from one vertex to a vertex adjacent orthogonally or diagonally.
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LINKS
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FORMULA
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Formula unknown, values computed empirically.
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PROG
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(Python)
def nn(c): # neighbors of c
i, j = divmod(c, 4)
N = set((i+io, j+jo) for io in [-1, 0, 1] for jo in [-1, 0, 1]) - {(i, j)}
return [4*i+j for i, j in N if 0 <= i < 4 and 0 <= j < 4]
def afind():
n, paths = 0, {(0, )}
while n+2 <= 16:
paths1 = set(p + (e, ) for p in paths for e in nn(p[-1]) if e not in p)
print(len(paths1), end=", ")
n, paths = n+1, paths1
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CROSSREFS
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KEYWORD
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fini,full,nonn
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AUTHOR
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Eugene McDonnell (EEMcD(AT)AOL.com), Jul 01 2001
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STATUS
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approved
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