cp's OEIS Frontend

A090031 Number of configurations of the 5 X 5 variant of sliding block 15-puzzle ("24-puzzle") that require a minimum of n moves to be reached, starting with the empty square in one of the corners.

%I A090031 #46 Jan 06 2025 22:29:18
%S A090031 1,2,4,10,26,64,159,366,862,1904,4538,10238,24098,53186,123435,268416,
%T A090031 616374,1326882,3021126,6438828,14524718,30633586,68513713,143106496,
%U A090031 317305688,656178756,1442068376,2951523620,6427133737,13014920506,28070588413,56212979470,120030667717
%N A090031 Number of configurations of the 5 X 5 variant of sliding block 15-puzzle ("24-puzzle") that require a minimum of n moves to be reached, starting with the empty square in one of the corners.
%C A090031 The 15-block puzzle is often referred to (incorrectly) as Sam Loyd's 15-Puzzle.
%C A090031 Sum of sequence terms = A088020(5)/2.
%C A090031 152 <= (number of last sequence term) <= 205 (see A087725 and cube archives link for current status).  - _Hugo Pfoertner_, Feb 12 2020
%D A090031 See A087725 for references.
%H A090031 Robert Clausecker, <a href="/A090031/a090031.c.txt">term generator puzzledist.c</a>
%H A090031 Robert Clausecker, <a href="http://nbn-resolving.de/urn:nbn:de:0297-zib-78489">The Quality of Heuristic Functions for IDA*</a>, Zuse Institute Berlin (2020).
%H A090031 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/sbpnxn.txt">Configuration counts for n*n sliding block puzzles.</a>
%H A090031 Tomas Rokicki, comment in <a href="http://forum.cubeman.org/?q=node/view/238">Twenty-Four puzzle, some observations</a>
%H A090031 Ben Whitmore in the Cube Forum, <a href="http://forum.cubeman.org/?q=node/view/559">5x5 sliding puzzle can be solved in 205 moves</a>, with updates by Johan de Ruiter claiming 182 moves.
%o A090031 (Fortran) ! See link in A089473.
%o A090031 (C) /* See Clausecker link. */
%o A090031 (Python) # alst(), moves(), swap() in A089473
%o A090031 start, shape = "-123456789ABCDEFGHIJKLMNO", (5, 5)
%o A090031 alst(start, shape, v=True) # _Michael S. Branicky_, Dec 31 2020
%Y A090031 Cf. A087725, A088020, A089473, A089484, A090032.
%K A090031 fini,hard,nonn
%O A090031 0,2
%A A090031 _Hugo Pfoertner_, Nov 25 2003
%E A090031 More terms from _Tomas Rokicki_, Aug 09 2011
%E A090031 a(28)-a(30) from _Robert Clausecker_, Jan 29 2018
%E A090031 a(31)-a(32) from _Robert Clausecker_, Sep 14 2020