A090166 Number of configurations of the 4 X 3 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, 4, 9, 20, 37, 63, 122, 232, 431, 781, 1392, 2494, 4442, 7854, 13899, 24215, 41802, 71167, 119888, 198363, 323206, 515778, 811000, 1248011, 1885279, 2782396, 4009722, 5621354, 7647872, 10065800, 12760413, 15570786, 18171606, 20299876, 21587248, 21841159, 20906905, 18899357, 16058335, 12772603, 9515217, 6583181, 4242753, 2503873, 1350268, 643245, 270303, 92311, 27116, 5390, 1115, 86, 18

Offset: 0

Author

Hugo Pfoertner, Nov 27 2003, Jul 07 2007

Keywords

• fini
• full
• nonn

Comments

Data from Karlemo and Östergård.

Links

• Filip R. W. Karlemo and Patric R. J. Östergård, On Sliding Block Puzzles, J. Combin. Math. Combin. Comp. 34 (2000), 97-107.
• Takaken, 11-Puzzle Page.
• Takaken, No. 43 (11 puzzles).

Crossrefs

Cf. A087725. Index of last sequence term: A090033. Other nonsquare sliding block puzzles: A090034, A090035, A090036, A090167.

Programs

Python

# alst(), moves(), swap() in A089473
alst("-123456789AB", (4, 3), v=True) # Michael S. Branicky, Dec 31 2020