A355560 Number of configurations of the 8 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, 68, 125, 227, 394, 672, 1151, 1983, 3373, 5703, 9508, 15640, 25293, 40732, 65032, 103390, 162830, 255543, 397013, 613104, 938477, 1431068, 2162964, 3255845, 4860428, 7223861, 10649867, 15628073, 22747718, 32963838, 47397514, 67825949, 96317070

Offset: 0

Author

Ben Whitmore, Jul 06 2022

Keywords

• nonn
• fini
• full

Comments

This sequence was computed by Richard Korf in "Linear-time Disk-Based Implicit Graph Search" (see links), but was not included in the paper.

Examples

			Starting from the solved configuration
   1  2  3  4  5  6  7  8
   9 10 11 12 13 14 15
the unique configuration requiring 140 moves is
      8  6  5  4  3 10  1
  15  7 14 13 12 11  2  9
		

Links

• Ben Whitmore, Table of n, a(n) for n = 0..140
• Richard Korf, Linear-time Disk-Based Implicit Graph Search, Journal of the ACM 55 (2008), No. 6.

Crossrefs

Cf. A090033, A090034, A090035, A090036, A090167, A346736.

Programs

Python

# alst(), moves(), swap() in A089473
print(alst("-123456789abcdef", (8, 2), v=True)) # Michael S. Branicky, Jul 06 2022