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

0,2

Comments

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

References

See A087725.

Links

Table of n, a(n) for n=0..36.

Hugo Pfoertner, Solutions of small n*2 sliding block puzzles.

Takaken, n-Puzzle Page.

Takaken, No. 42 (7 puzzles).

Example

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

Prog

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

Crossrefs

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

Sequence in context: A190690 A355509 A084396 * A337611 A325724 A111467

Adjacent sequences: A090032 A090033 A090034 * A090036 A090037 A090038

Keyword

fini,full,nonn

Author

Hugo Pfoertner, Nov 26 2003

Status

approved