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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 09:06 EDT 2021. Contains 343087 sequences. (Running on oeis4.)