

A063000


Number of paths of length n+2 originating at a corner of a 4 X 4 Boggle board.


3



3, 15, 75, 322, 1184, 3814, 10918, 27772, 61734, 116966, 183256, 228016, 211502, 128994, 37948
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OFFSET

0,1


COMMENTS

A legal walk on a Boggle board is from one vertex to a vertex adjacent orthogonally or diagonally.


LINKS

Table of n, a(n) for n=0..14.
Eugene McDonnell, Remarks on Game of "Boggle"


FORMULA

Formula unknown, values computed empirically.


PROG

(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
afind() # Michael S. Branicky, Mar 15 2021


CROSSREFS

Cf. A063001, A063002.
Sequence in context: A224397 A190010 A151326 * A002902 A236579 A005053
Adjacent sequences: A062997 A062998 A062999 * A063001 A063002 A063003


KEYWORD

fini,full,nonn


AUTHOR

Eugene McDonnell (EEMcD(AT)AOL.com), Jul 01 2001


STATUS

approved



