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Number of configurations of the 3 X 2 variant of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.
+10
9
1, 2, 3, 5, 6, 7, 10, 12, 12, 16, 23, 25, 28, 39, 44, 40, 29, 21, 18, 12, 6, 1
COMMENTS
Data from Karlemo and Östergård. See corresponding link in A087725.
EXAMPLE
Starting with
123
45-
the most distant configuration corresponding to a(21)=1 is
45-
123 (i.e., it takes longest just to swap the two rows).
PROG
(Python) # alst(), moves(), swap() in A089473
Number of configurations of the 5 X 2 variant of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.
+10
9
1, 2, 3, 6, 11, 19, 30, 44, 68, 112, 176, 271, 411, 602, 851, 1232, 1783, 2530, 3567, 4996, 6838, 9279, 12463, 16597, 21848, 28227, 35682, 44464, 54597, 65966, 78433, 91725, 104896, 116966, 126335, 131998, 133107, 128720, 119332, 106335, 91545, 75742, 60119, 45840, 33422, 23223, 15140, 9094, 5073, 2605, 1224, 528, 225, 75, 20, 2
EXAMPLE
Starting from
12345
6789-
the 2 most distant configurations corresponding to a(55)=2 are
-9371 and -5321
54826.....94876
PROG
(Python) # alst(), moves(), swap() in A089473
Number of configurations of the 4 X 2 variant of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.
+10
8
1, 2, 3, 6, 10, 14, 19, 28, 42, 61, 85, 119, 161, 215, 293, 396, 506, 632, 788, 985, 1194, 1414, 1664, 1884, 1999, 1958, 1770, 1463, 1076, 667, 361, 190, 88, 39, 19, 7, 1
COMMENTS
Data from Karlemo, Östergård. See corresponding link in A087725.
EXAMPLE
Starting from
1234
567-
the most distant configuration corresponding to a(36)=1 is
-721
4365
PROG
(Python) # alst(), moves(), swap() in A089473
Number of configurations of the 4 X 3 variant of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.
+10
5
1, 2, 4, 9, 20, 37, 63, 122, 232, 431, 781, 1392, 2494, 4442, 7854, 13899, 24215, 41802, 71167, 119888, 198363, 323206, 515778, 811000, 1248011, 1885279, 2782396, 4009722, 5621354, 7647872, 10065800, 12760413, 15570786, 18171606, 20299876, 21587248, 21841159, 20906905, 18899357, 16058335, 12772603, 9515217, 6583181, 4242753, 2503873, 1350268, 643245, 270303, 92311, 27116, 5390, 1115, 86, 18
COMMENTS
Data from Karlemo and Östergård.
LINKS
Filip R. W. Karlemo and Patric R. J. Östergård, On Sliding Block Puzzles, J. Combin. Math. Combin. Comp. 34 (2000), 97-107.
PROG
(Python) # alst(), moves(), swap() in A089473
Number of configurations of the 7 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.
+10
3
1, 2, 3, 6, 11, 20, 37, 67, 117, 198, 329, 557, 942, 1575, 2597, 4241, 6724, 10535, 16396, 25515, 39362, 60532, 92089, 138969, 207274, 307725, 453000, 664240, 964874, 1392975, 1992353, 2832063, 3988528, 5586275, 7756511, 10698721, 14621717, 19840724, 26676629
COMMENTS
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.
EXAMPLE
Starting from the solved configuration
1 2 3 4 5 6 7
8 9 10 11 12 13
the unique configuration requiring 108 moves is
7 6 12 4 3 9 1
13 5 11 10 2 8
PROG
(Python) # alst(), moves(), swap() in A089473
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.
+10
1
1, 2, 4, 9, 21, 42, 89, 164, 349, 644, 1349, 2473, 5109, 9110, 18489, 32321, 64962, 112445, 223153, 378761, 740095, 1231589, 2364342, 3847629, 7246578, 11506172, 21233764, 32854049, 59293970, 89146163, 157015152, 228894783, 392648931, 553489877, 922382155
COMMENTS
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.
EXAMPLE
Starting from the solved configuration
1 2 3 4 5
6 7 8 9 10
11 12 13 14
the unique configuration requiring 84 moves is
5 4 3 2 1
10 9 8 7 6
14 13 12 11
PROG
(Python) # alst(), moves(), swap() in A089473
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.
+10
1
1, 2, 3, 6, 11, 20, 37, 68, 125, 227, 394, 672, 1151, 1983, 3373, 5703, 9508, 15640, 25293, 40732, 65032, 103390, 162830, 255543, 397013, 613104, 938477, 1431068, 2162964, 3255845, 4860428, 7223861, 10649867, 15628073, 22747718, 32963838, 47397514, 67825949, 96317070
COMMENTS
This sequence was computed by Richard Korf in "Linear-time Disk-Based Implicit Graph Search" (see links), but was not included in the paper.
EXAMPLE
Starting from the solved configuration
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15
the unique configuration requiring 140 moves is
8 6 5 4 3 10 1
15 7 14 13 12 11 2 9
PROG
(Python) # alst(), moves(), swap() in A089473
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