A389729 Number of positions of the 8 X 2 variant of the 15-puzzle at a distance of n multi-tile moves from an initial state with the empty square in one of the corners.

1, 8, 14, 56, 98, 392, 685, 2688, 4552, 15120, 25736, 85280, 142472, 449216, 746786, 2286992, 3776238, 11015896, 17976999, 50832504, 82322380, 221230656, 352869190, 911581064, 1437928475, 3505471976, 5416379388, 12529508408, 18999577833, 40787934216

Offset

0,2

Comments

A multi-tile move shifts a group of tiles so that the empty square moves to anywhere within its existing row, or existing column.

This is a finite sequence ending at a(57) = 80.

Links

Ben Whitmore, Table of n, a(n) for n = 0..57

Oleg Tarakanov, Complete Breadth-First Search of the Sliding Tile Puzzles

Formula

Sum_{i=0..57} a(i) = 16!/2.

Crossrefs

Cf. A355560 (single-tile moves), A389728.

Sequence in context: A198307 A218555 A268160 * A236553 A050582 A128451

Adjacent sequences: A389726 A389727 A389728 * A389730 A389731 A389732

Keyword

nonn,fini,full

Author

Ben Whitmore, Jan 09 2026

Status

approved