cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A090576 Number of configurations 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 mid-side of one of the 12 edges of the combination cube.

Original entry on oeis.org

1, 4, 12, 40, 128, 412, 1251, 4026, 12362, 39624, 120012, 379132, 1130914, 3530916, 10402781, 32112656, 93427431
Offset: 0

Views

Author

Hugo Pfoertner, Jan 15 2004

Keywords

Comments

See under A090573.

Examples

			a(1)=4 because the empty space located at mid-edge of one of the 12 edges of the assumed initial configuration can be replaced in the first move by any of the adjacent 2 cubes from the same edge or by the adjacent mid-face cubes of the 2 faces forming this edge.

Crossrefs

Cf. A090572 2 X 2 X 2 puzzle, A090573, A090574, A090575 3 X 3 X 3 puzzle with different initial configurations.

Programs

  • Python
    # uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

Extensions

a(13)-a(16) from Michael S. Branicky, Dec 28 2020

A090166 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.

Original entry on oeis.org

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
Offset: 0

Views

Author

Hugo Pfoertner, Nov 27 2003, Jul 07 2007

Keywords

Comments

Data from Karlemo and Östergård.

Links

Crossrefs

Cf. A087725. Index of last sequence term: A090033. Other nonsquare sliding block puzzles: A090034, A090035, A090036, A090167.

Programs

A089483 Number of configurations of the sliding block 8-puzzle that require a minimum of n moves to be reached, starting with the empty square at mid-side.

Original entry on oeis.org

1, 3, 5, 10, 14, 28, 42, 80, 108, 202, 278, 524, 726, 1348, 1804, 3283, 4193, 7322, 8596, 13930, 14713, 21721, 19827, 25132, 18197, 18978, 9929, 7359, 2081, 878, 126, 2
Offset: 0

Views

Author

Hugo Pfoertner, Nov 19 2003

Keywords

Examples

			Starting with
1-2
345
678
the two final configurations requiring 31 moves are
86- ... -86
547 and 743
231 ... 251

References

Links

Crossrefs

Cf. A089473, A089474, A089484, A087725, A090031.

Programs

A090032 Number of configurations of the 6 X 6 variant of Sam Loyd's sliding block 15-puzzle ("35-puzzle") that require a minimum of n moves to be reached, starting with the empty square in one of the corners.

Original entry on oeis.org

1, 2, 4, 10, 26, 66, 171, 440, 1112, 2786, 6820, 16720, 41106, 100856, 245793, 597030, 1441292, 3469486, 8304526, 19832076, 47110238, 111669014
Offset: 0

Views

Author

Hugo Pfoertner, Nov 25 2003

Keywords

References

Links

Crossrefs

Cf. A087725, A089473, A089484, A090031.

Programs

  • Python
    # uses alst(), swap() in A089473
start, shape = "-123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ", (6, 6)
print(alst(start, shape, maxd=16)) # Michael S. Branicky, Jan 02 2021

Extensions

a(17)-a(21) from Michael S. Branicky, Dec 28 2020

A090165 Number of configurations of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square at one of the 8 non-corner boundary squares.

Original entry on oeis.org

1, 3, 6, 14, 32, 66, 134, 280, 585, 1214, 2462, 4946, 9861, 19600, 38688, 76086, 148435, 288098, 554970, 1062628, 2016814, 3800682, 7093209, 13127364, 24053454, 43657576, 78382622, 139237375
Offset: 0

Views

Author

Hugo Pfoertner, Nov 27 2003

Keywords

Crossrefs

Cf. A087725, A089473, A089484, A090164, A090378.

Programs

  • Python
    # uses alst(), swap() in A089473
start, shape = "1-23456789ABCDEF", (4, 4)
print(alst(start, shape, maxd=16)) # Michael S. Branicky, Jan 02 2021

Extensions

a(17)-a(27) from Michael S. Branicky, Dec 28 2020

A090574 Number of configurations 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 in the center of the combination cube.

Original entry on oeis.org

1, 6, 24, 72, 192, 624, 2004, 6504, 19776, 62760, 186000, 583712, 1720972, 5344088, 15565416, 47816092, 137916958
Offset: 0

Views

Author

Hugo Pfoertner, Jan 15 2004

Keywords

Comments

See under A090573.

Examples

			a(1)=6 because the empty space in the center of the cube present in the assumed initial configuration can be replaced by any of the 6 adjacent cubes from the face centers in the first move.

Crossrefs

A090572 2 X 2 X 2 puzzle, A090573, A090575, A090576 3 X 3 X 3 puzzle with different initial configurations.

Programs

  • Python
    # uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "123456789ABCD-EFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

Extensions

a(13)-a(16) from Michael S. Branicky, Dec 28 2020

A090575 Number of configurations 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 the center of one of the 6 faces of the combination cube.

Original entry on oeis.org

1, 5, 17, 52, 164, 496, 1608, 5008, 16024, 48732, 153564, 460984, 1437632, 4263236, 13150544, 38498798, 117497284
Offset: 0

Views

Author

Hugo Pfoertner, Jan 15 2004

Keywords

Comments

See A090573.

Examples

			a(1)=5 because the empty space located at the center of a face of the combination cube in the assumed initial configuration can be replaced in the first move by either the cube from the center of the combination cube or by one of the 4 adjacent cubes located at the edges of the face initially containing the empty space.

Crossrefs

A090572 2 X 2 X 2 puzzle, A090573, A090574, A090576 3 X 3 X 3 puzzle with different initial configurations.

Programs

  • Python
    # uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "1234-56789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

Extensions

a(13)-a(16) from Michael S. Branicky, Dec 28 2020

A090578 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 mid-edge of one of the 12 edges of the combination cube.

Original entry on oeis.org

1, 4, 10, 30, 74, 222, 546, 1628, 3978, 11810, 28658, 84520, 203562, 596520, 1425924, 4150232, 9838116, 28418002, 66805554
Offset: 0

Views

Author

Hugo Pfoertner, Jan 19 2004

Keywords

Comments

See under A090577.

Examples

			a(1)=4 because the empty space located at mid-edge of one of the 12 edges of the assumed initial configuration can be replaced in the first move by any of the adjacent 2 cubes from the same edge or by the adjacent mid-face cubes of the 2 faces forming this edge.

Crossrefs

Cf. A090577, 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.

Programs

  • Python
    # uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=13)) # Michael S. Branicky, Dec 28 2020

Extensions

a(14)-a(18) from Michael S. Branicky, Dec 28 2020

A346736 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.

Original entry on oeis.org

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
Offset: 0

Views

Author

Ben Whitmore, Jul 31 2021

Keywords

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.

Examples

			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

Links

Crossrefs

Cf. A090033, A090034, A090035, A090036, A090167, A089473, A089484.

Programs

A089474 Number of configurations of the sliding block 8-puzzle that require a minimum of n moves to be reached, starting with the empty square in the center.

Original entry on oeis.org

1, 4, 8, 8, 16, 32, 60, 72, 136, 200, 376, 512, 964, 1296, 2368, 3084, 5482, 6736, 11132, 12208, 18612, 18444, 24968, 19632, 22289, 13600, 11842, 4340, 2398, 472, 148
Offset: 0

Views

Author

Hugo Pfoertner, Nov 19 2003

Keywords

Examples

			Starting with
123
4-5
678
two of the 148 configurations that require the maximum of 30 moves are
476 ... -86
2-8 and 724
351 ... 351

References

Links

Crossrefs

Cf. A089473, A089483, A089484, A087725, A090031.

Programs

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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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