A063001 Number of paths of length n+2 originating at a non-corner edge of 4 X 4 Boggle board.

5, 24, 109, 435, 1512, 4621, 12463, 29565, 60596, 104542, 147032, 161759, 130777, 68989, 17681

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, {(1, )}
  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, May 24 2021

Crossrefs

Cf. A063000, A063002.

Sequence in context: A270186 A008464 A291010 * A000953 A183934 A171310

Adjacent sequences: A062998 A062999 A063000 * A063002 A063003 A063004

Keyword

fini,full,nonn

Author

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

Status

approved