A089483 Number of configurations of the sliding block 8-puzzle that require a minimum of n moves to be reached, starting with the empty square at mid-side.

1, 3, 5, 10, 14, 28, 42, 80, 108, 202, 278, 524, 726, 1348, 1804, 3283, 4193, 7322, 8596, 13930, 14713, 21721, 19827, 25132, 18197, 18978, 9929, 7359, 2081, 878, 126, 2

Offset

0,2

References

See A087725.

Links

Table of n, a(n) for n=0..31.

Hugo Pfoertner, Table of solution lengths of the 8-puzzle

Example

Starting with
1-2
345
678
the two final configurations requiring 31 moves are
86- ... -86
547 and 743
231 ... 251

Maple

See link in A089473.

Prog

(Python) # alst(), moves(), swap() in A089473
print(alst("1-2345678", (3, 3))) # Michael S. Branicky, Dec 30 2020

Crossrefs

Cf. A089473, A089474, A089484, A087725, A090031.

Sequence in context: A306319 A182722 A365379 * A323858 A190484 A190545

Adjacent sequences: A089480 A089481 A089482 * A089484 A089485 A089486

Keyword

fini,full,nonn

Author

Hugo Pfoertner, Nov 19 2003

Status

approved