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

0,2

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..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.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A065615 A054182 A358709 * A335628 A355560 A001590

Adjacent sequences: A346733 A346734 A346735 * A346737 A346738 A346739

Keyword

nonn,fini,full

Author

Ben Whitmore, Jul 31 2021

Status

approved