A089474 Number of configurations of the sliding block 8-puzzle that require a minimum of n moves to be reached, starting with the empty square in the center.

1, 4, 8, 8, 16, 32, 60, 72, 136, 200, 376, 512, 964, 1296, 2368, 3084, 5482, 6736, 11132, 12208, 18612, 18444, 24968, 19632, 22289, 13600, 11842, 4340, 2398, 472, 148

Offset

0,2

References

See A087725.

Links

Table of n, a(n) for n=0..30.

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

Example

Starting with
123
4-5
678
two of the 148 configurations that require the maximum of 30 moves are
476 ... -86
2-8 and 724
351 ... 351

Maple

See link in A089473.

Prog

(Python) # alst(), moves(), swap() in A089473
print(alst("1234-5678", (3, 3))) # Michael S. Branicky, Dec 30 2020

Crossrefs

Cf. A089473, A089483, A089484, A087725, A090031.

Sequence in context: A354455 A209382 A298119 * A141800 A019197 A066106

Adjacent sequences: A089471 A089472 A089473 * A089475 A089476 A089477

Keyword

fini,full,nonn

Author

Hugo Pfoertner, Nov 19 2003

Status

approved