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%I #10 Dec 29 2020 06:33:22
%S 1,3,9,24,72,174,519,1284,3813,9300,27462,66666,195674,470886,1372946,
%T 3280224,9495005,22487511,64615934,151714911
%N Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at one of the enclosing cube corners.
%C The sliding cube 3 X 3 X 3 puzzle under consideration has a fixed central block and 25 movable blocks that can be shifted in the space between the enclosing holder frame and the central block. A description is given in US patents 3845959 and 6513808.
%H Chih Chung Fang, <a href="http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=6513808">Cubic Puzzle.</a> US Patent 6513808, filed May 09, 2001
%H Daniel Kosarek, <a href="http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=3845959">Three-dimensional block puzzle.</a> US Patent 3845959, filed Nov. 5, 1974
%e a(1)=3 because the empty space at one of the 6 corners in the assumed initial configuration can be replaced by any of the 3 adjacent cubes from the middle of the 3 edges meeting at the empty corner in the first move.
%o (Python) # uses alst(), swap() in A089473, moves3d() in A090573
%o moves = lambda p, shape: moves3d(p, shape, fixed=13)
%o start, shape = "-123456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
%o print(alst(start, shape, maxd=14)) # _Michael S. Branicky_, Dec 28 2020
%Y Cf. A090578, A091521 this puzzle with different initial configurations, A090572 2X2X2 puzzle, A090573 - A090576 configurations of the 3 X 3 X 3 puzzle with 26 movable blocks.
%K fini,hard,more,nonn
%O 0,2
%A _Hugo Pfoertner_, Jan 19 2004
%E a(15)-a(19) from _Michael S. Branicky_, Dec 28 2020
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