A090036 Number of configurations of the 5 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, 11, 19, 30, 44, 68, 112, 176, 271, 411, 602, 851, 1232, 1783, 2530, 3567, 4996, 6838, 9279, 12463, 16597, 21848, 28227, 35682, 44464, 54597, 65966, 78433, 91725, 104896, 116966, 126335, 131998, 133107, 128720, 119332, 106335, 91545, 75742, 60119, 45840, 33422, 23223, 15140, 9094, 5073, 2605, 1224, 528, 225, 75, 20, 2

Offset

0,2

Links

Table of n, a(n) for n=0..55.

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

Takaken, 11-Puzzle Page.

Takaken, No. 52 (9 puzzles).

Example

Starting from
12345
6789-
the 2 most distant configurations corresponding to a(55)=2 are
-9371 and -5321
54826.....94876

Prog

See link in A089473.
(Python) # alst(), moves(), swap() in A089473
print(alst("-123456789", (5, 2))) # Michael S. Branicky, Dec 30 2020

Crossrefs

Cf. A087725, A089473. Index of last sequence term: A090033. Other nonsquare sliding block puzzles: A090034, A090035, A090166, A090167.

Sequence in context: A039827 A004135 A288583 * A024971 A038084 A018169

Adjacent sequences: A090033 A090034 A090035 * A090037 A090038 A090039

Keyword

fini,full,nonn

Author

Hugo Pfoertner, Nov 27 2003

Status

approved