A346737 Number of configurations of the 5 X 3 variant of the 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, 21, 42, 89, 164, 349, 644, 1349, 2473, 5109, 9110, 18489, 32321, 64962, 112445, 223153, 378761, 740095, 1231589, 2364342, 3847629, 7246578, 11506172, 21233764, 32854049, 59293970, 89146163, 157015152, 228894783, 392648931, 553489877, 922382155

Offset

0,2

Comments

This sequence was originally computed by Richard Korf, but the full sequence was not included in his paper. It was later re-computed by Tomas Rokicki.

Links

Ben Whitmore, Table of n, a(n) for n = 0..84

Richard Korf, Linear-time Disk-Based Implicit Graph Search, Journal of the ACM 55 (2008), No. 6.

Tomas Rokicki, Twenty-Four puzzle, some observations, 2011.

Example

Starting from the solved configuration
   1  2  3  4  5
   6  7  8  9 10
  11 12 13 14
the unique configuration requiring 84 moves is
   5  4  3  2  1
  10  9  8  7  6
     14 13 12 11

Prog

(Python) # alst(), moves(), swap() in A089473
print(alst("-123456789abcde", (5, 3), v=True)) # Michael S. Branicky, Jul 31 2021

Crossrefs

Cf. A090033, A090034, A090035, A090036, A090167, A346736, A090166, A089473, A089484.

Sequence in context: A034750 A079060 A225173 * A030039 A018105 A035056

Adjacent sequences: A346734 A346735 A346736 * A346738 A346739 A346740

Keyword

nonn,fini,full

Author

Ben Whitmore, Jul 31 2021

Status

approved