A079875 Number of positions that are exactly n moves from the starting position in the Lights Out 2000 puzzle.

1, 25, 325, 2900, 19850, 110630, 520948, 2125078, 7644164, 24561916, 71147752, 186876765, 446015084, 964537892, 1872111656, 3203446007, 4709112417, 5767439109, 5710406148, 4433675458, 2590026921, 1073252214, 279734731, 36143633, 2147985

Offset

0,2

Comments

This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves.

A puzzle in the Rubik cube family. The total number of distinct positions is 31381059609.

Links

Table of n, a(n) for n=0..24.

Jaap Scherphuis, Puzzle Pages

Prog

(Python) # alst(), moves() in A079873
shape, states = (5, 5), 3  # 5x5 with off-red-green states
start = tuple([0 for i in range(shape[0]*shape[1])])
print(alst(start, shape, states, v=True)) # Michael S. Branicky, Jan 25 2021

Crossrefs

Sequence in context: A124980 A188355 A243089 * A162702 A010977 A022589

Adjacent sequences: A079872 A079873 A079874 * A079876 A079877 A079878

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Feb 21 2003

Status

approved