A090035 Number of configurations of the 4 X 2 variant of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.

1, 2, 3, 6, 10, 14, 19, 28, 42, 61, 85, 119, 161, 215, 293, 396, 506, 632, 788, 985, 1194, 1414, 1664, 1884, 1999, 1958, 1770, 1463, 1076, 667, 361, 190, 88, 39, 19, 7, 1

Offset: 0

Author

Hugo Pfoertner, Nov 26 2003

Keywords

• fini
• full
• nonn

Comments

Data from Karlemo, Östergård. See corresponding link in A087725.

Examples

			Starting from
1234
567-
the most distant configuration corresponding to a(36)=1 is
-721
4365
		

References

• See A087725.

Links

• Hugo Pfoertner, Solutions of small n*2 sliding block puzzles.
• Takaken, n-Puzzle Page.
• Takaken, No. 42 (7 puzzles).

Crossrefs

Cf. A087725, A089473. Index of last sequence term: A090033. Other nonsquare sliding block puzzles: A090034, A090036, A090166, A090167.

Programs

Python

# alst(), moves(), swap() in A089473
print(alst("-1234567", (4, 2))) # Michael S. Branicky, Dec 30 2020