cp's OEIS Frontend

A346737 Number of configurations of the 5 X 3 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.

%I A346737 #24 Aug 03 2021 12:43:43
%S A346737 1,2,4,9,21,42,89,164,349,644,1349,2473,5109,9110,18489,32321,64962,
%T A346737 112445,223153,378761,740095,1231589,2364342,3847629,7246578,11506172,
%U A346737 21233764,32854049,59293970,89146163,157015152,228894783,392648931,553489877,922382155
%N A346737 Number of configurations of the 5 X 3 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 A346737 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_.
%H A346737 Ben Whitmore, <a href="/A346737/b346737.txt">Table of n, a(n) for n = 0..84</a>
%H A346737 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.
%H A346737 Tomas Rokicki, <a href="http://forum.cubeman.org/?q=node/view/238">Twenty-Four puzzle, some observations</a>, 2011.
%e A346737 Starting from the solved configuration
%e A346737    1  2  3  4  5
%e A346737    6  7  8  9 10
%e A346737   11 12 13 14
%e A346737 the unique configuration requiring 84 moves is
%e A346737    5  4  3  2  1
%e A346737   10  9  8  7  6
%e A346737      14 13 12 11
%o A346737 (Python) # alst(), moves(), swap() in A089473
%o A346737 print(alst("-123456789abcde", (5, 3), v=True)) # _Michael S. Branicky_, Jul 31 2021
%Y A346737 Cf. A090033, A090034, A090035, A090036, A090167, A346736, A090166, A089473, A089484.
%K A346737 nonn,fini,full
%O A346737 0,2
%A A346737 _Ben Whitmore_, Jul 31 2021