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

0,2

Comments

Data from Karlemo and Östergård.

Links

Table of n, a(n) for n=0..53.

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).

Prog

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

Crossrefs

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

Sequence in context: A353734 A053024 A240047 * A101338 A018102 A018103

Adjacent sequences: A090163 A090164 A090165 * A090167 A090168 A090169

Keyword

fini,full,nonn

Author

Hugo Pfoertner, Nov 27 2003, Jul 07 2007

Status

approved