A346736 Number of configurations of the 7 X 2 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, 3, 6, 11, 20, 37, 67, 117, 198, 329, 557, 942, 1575, 2597, 4241, 6724, 10535, 16396, 25515, 39362, 60532, 92089, 138969, 207274, 307725, 453000, 664240, 964874, 1392975, 1992353, 2832063, 3988528, 5586275, 7756511, 10698721, 14621717, 19840724, 26676629

Offset: 0

Author

Ben Whitmore, Jul 31 2021

Keywords

• nonn
• fini
• full

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.

Examples

			Starting from the solved configuration
  1  2  3  4  5  6  7
  8  9 10 11 12 13
the unique configuration requiring 108 moves is
  7  6 12  4  3  9  1
    13  5 11 10  2  8
		

Links

• Ben Whitmore, Table of n, a(n) for n = 0..108
• 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.

Crossrefs

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

Programs

Python

# alst(), moves(), swap() in A089473
print(alst("-123456789abcd", (7, 2), v=True)) # Michael S. Branicky, Jul 31 2021