%I #16 Sep 04 2022 12:24:48

%S 1,2,3,6,11,20,37,68,125,227,394,672,1151,1983,3373,5703,9508,15640,

%T 25293,40732,65032,103390,162830,255543,397013,613104,938477,1431068,

%U 2162964,3255845,4860428,7223861,10649867,15628073,22747718,32963838,47397514,67825949,96317070

%N 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.

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

%H Ben Whitmore, <a href="/A355560/b355560.txt">Table of n, a(n) for n = 0..140</a>

%H Richard Korf, <a href="https://www.cs.helsinki.fi/u/bmmalone/heuristic-search-fall-2013/Korf2008.pdf">Linear-time Disk-Based Implicit Graph Search</a>, Journal of the ACM 55 (2008), No. 6.

%e Starting from the solved configuration

%e 1 2 3 4 5 6 7 8

%e 9 10 11 12 13 14 15

%e the unique configuration requiring 140 moves is

%e 8 6 5 4 3 10 1

%e 15 7 14 13 12 11 2 9

%o (Python) # alst(), moves(), swap() in A089473

%o print(alst("-123456789abcdef", (8, 2), v=True)) # _Michael S. Branicky_, Jul 06 2022

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

%K nonn,fini,full

%O 0,2

%A _Ben Whitmore_, Jul 06 2022