A389729 - OEIS

%I #17 Jan 21 2026 21:03:53

%S 1,8,14,56,98,392,685,2688,4552,15120,25736,85280,142472,449216,

%T 746786,2286992,3776238,11015896,17976999,50832504,82322380,221230656,

%U 352869190,911581064,1437928475,3505471976,5416379388,12529508408,18999577833,40787934216

%N 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.

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

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

%H Ben Whitmore, <a href="/A389729/b389729.txt">Table of n, a(n) for n = 0..57</a>

%H Oleg Tarakanov, <a href="https://github.com/lightln2/SlidingTilesSolver">Complete Breadth-First Search of the Sliding Tile Puzzles</a>

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

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

%K nonn,fini,full

%O 0,2

%A _Ben Whitmore_, Jan 09 2026