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.

Showing 1-7 of 7 results.

A186441 Number of n-vertex knight's tours on the 8x8 chessboard summed over all choices for the starting position.

Original entry on oeis.org

64, 336, 1672, 8320, 39616, 186544, 847520, 3846192, 16784384, 72946352, 304472976, 1265186112
Offset: 1

Views

Author

N. J. A. Sloane, Feb 21 2011

Keywords

Examples

			a(1) = 64, since the knight cannot move.

References

  • L. Lant, A method for calculating the Knight's total tour count, Congress. Numerant., 202 (2010), 33-40. [Lant comments that "a(5)=40208 has not yet been verified."]

Links

Crossrefs

Cf. A001230.
Column 6 of A186851

Programs

Extensions

a(5) to a(8) are tabulated here as computed by R. H. Hardin and D. S. McNeil.
Ambiguous a(0) removed by Max Alekseyev, Sep 22 2013
a(9)-a(12) from Andrew Howroyd, Jan 02 2023

A186852 Number of 3-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Original entry on oeis.org

16, 104, 328, 664, 1112, 1672, 2344, 3128, 4024, 5032, 6152, 7384, 8728, 10184, 11752, 13432, 15224, 17128, 19144, 21272, 23512, 25864, 28328, 30904, 33592, 36392, 39304, 42328, 45464, 48712, 52072, 55544, 59128, 62824, 66632, 70552, 74584, 78728, 82984, 87352
Offset: 1

Views

Author

R. H. Hardin, Feb 27 2011

Keywords

Examples

			Some solutions for 5 X 5:
  0 0 0 0 0    3 0 0 0 0    0 0 0 3 0    0 0 3 0 0
  0 1 0 0 0    0 0 2 0 0    0 2 0 0 0    0 1 0 0 0
  0 0 0 2 0    0 0 0 0 1    0 0 0 0 0    0 0 0 2 0
  0 0 0 0 0    0 0 0 0 0    0 0 1 0 0    0 0 0 0 0
  0 0 0 0 3    0 0 0 0 0    0 0 0 0 0    0 0 0 0 0

Links

Crossrefs

Row 3 of A186851.

Programs

Formula

Empirical: a(n) = 56*n^2 - 56*n - 8 for n > 1.
The above empirical formula is correct. See A186851 for details. - Andrew Howroyd, Jan 07 2023

Extensions

Terms a(27) and beyond from Andrew Howroyd, Jan 07 2023

A186853 Number of 4-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Original entry on oeis.org

16, 208, 976, 2576, 5056, 8320, 12368, 17200, 22816, 29216, 36400, 44368, 53120, 62656, 72976, 84080, 95968, 108640, 122096, 136336, 151360, 167168, 183760, 201136, 219296, 238240, 257968, 278480, 299776, 321856, 344720, 368368, 392800
Offset: 1

Views

Author

R. H. Hardin, Feb 27 2011

Keywords

Examples

			Some solutions for 5 X 5:
  0 1 0 0 0    0 3 0 0 0    0 0 0 0 0    0 0 1 0 0
  0 0 3 0 0    0 0 0 0 0    0 0 0 0 1    4 0 0 0 2
  2 0 0 0 4    4 0 2 0 0    4 0 0 0 0    0 0 3 0 0
  0 0 0 0 0    0 0 0 0 0    0 0 0 2 0    0 0 0 0 0
  0 0 0 0 0    0 0 0 1 0    0 3 0 0 0    0 0 0 0 0

Links

Crossrefs

Row 4 of A186851.

Programs

Formula

Empirical: a(n) = 392*n^2 - 1048*n + 496 for n > 3.
The above empirical formula is correct. See A186851 for details. - Andrew Howroyd, Jan 07 2023

A186854 Number of 5-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Original entry on oeis.org

16, 400, 2800, 9328, 21480, 39616, 63440, 92656, 127264, 167264, 212656, 263440, 319616, 381184, 448144, 520496, 598240, 681376, 769904, 863824, 963136, 1067840, 1177936, 1293424, 1414304, 1540576, 1672240, 1809296, 1951744, 2099584, 2252816, 2411440
Offset: 1

Views

Author

R. H. Hardin, Feb 27 2011

Keywords

Examples

			Some solutions for 5 X 5:
  0 0 0 0 1    0 2 0 0 0    0 5 0 0 0    0 1 0 0 0
  0 3 0 0 0    0 0 0 3 0    0 0 0 2 0    3 0 0 0 0
  0 0 0 2 0    1 0 0 0 0    4 0 0 0 0    0 0 2 5 0
  0 0 4 0 0    0 0 4 0 0    0 0 3 0 1    0 4 0 0 0
  0 0 0 0 5    0 0 0 0 5    0 0 0 0 0    0 0 0 0 0

Links

Crossrefs

Row 5 of A186851.

Programs

Formula

Empirical: a(n) = 2696*n^2 - 11224*n + 9904 for n > 5.
The above empirical formula is correct. See A186851 for details. - Andrew Howroyd, Jan 07 2023

Extensions

Terms a(25) and beyond from Andrew Howroyd, Jan 07 2023

A186855 Number of 6-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Original entry on oeis.org

16, 800, 8352, 34448, 91328, 186544, 322528, 498320, 712080, 963008, 1251104, 1576368, 1938800, 2338400, 2775168, 3249104, 3760208, 4308480, 4893920, 5516528, 6176304, 6873248, 7607360, 8378640, 9187088, 10032704, 10915488, 11835440, 12792560, 13786848
Offset: 1

Views

Author

R. H. Hardin, Feb 27 2011

Keywords

Examples

			Some solutions for 5 X 5:
  0 0 0 0 6     1 0 0 0 0     0 4 0 0 0     0 0 0 0 0
  0 0 5 2 0     0 0 2 0 6     0 0 0 0 6     0 0 0 3 6
  0 3 0 0 0     3 0 0 0 0     3 0 5 0 1     0 4 1 0 0
  0 0 0 4 1     0 0 0 5 0     0 0 2 0 0     0 0 0 5 2
  0 0 0 0 0     0 4 0 0 0     0 0 0 0 0     0 0 0 0 0

Links

Crossrefs

Row 6 of A186851.

Programs

Formula

a(n) = 18584*n^2 - 102168*n + 126288 for n > 7.

Extensions

Terms a(16) and beyond from Andrew Howroyd, Jan 02 2023

A186856 Number of 7-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Original entry on oeis.org

16, 1280, 21664, 118480, 372384, 847520, 1584576, 2596480, 3879696, 5424848, 7224912, 9277856, 11583680, 14142384, 16953968, 20018432, 23335776, 26906000, 30729104, 34805088, 39133952, 43715696, 48550320, 53637824, 58978208, 64571472
Offset: 1

Views

Author

R. H. Hardin, Feb 27 2011

Keywords

Examples

			Some solutions for 5 X 5:
  0 1 0 0 0     2 0 0 0 0     0 0 0 1 0     2 0 0 0 0
  0 0 0 0 0     0 0 3 0 0     3 6 0 0 0     0 0 1 0 0
  0 5 2 0 0     0 1 6 0 0     0 0 2 5 0     0 3 6 0 0
  7 0 0 4 0     0 4 0 0 0     0 4 7 0 0     0 0 0 4 7
  0 3 6 0 0     0 7 0 5 0     0 0 0 0 0     0 5 0 0 0

Links

Crossrefs

Row 7 of A186851.

Programs

Formula

a(n) = 126440*n^2 - 855176*n + 1332608 for n >= 10. - Andrew Howroyd, Jan 02 2023

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 02 2023

A186857 Number of 8-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Original entry on oeis.org

16, 2208, 57392, 405040, 1508784, 3846192, 7777808, 13502064, 21089312, 30521216, 41748432, 54726992, 69434272, 85865344, 104020208, 123898864, 145501312, 168827552, 193877584, 220651408, 249149024, 279370432, 311315632, 344984624, 380377408, 417493984
Offset: 1

Views

Author

R. H. Hardin, Feb 27 2011

Keywords

Examples

			Some solutions for 5 X 5:
  0 0 0 0 0     0 3 8 0 0     0 0 0 4 7     3 0 5 0 0
  0 0 7 0 0     0 0 0 0 0     2 5 8 0 0     6 0 2 0 0
  0 0 2 5 0     2 0 4 7 0     0 0 3 6 0     0 4 7 0 1
  3 6 0 8 0     0 6 0 0 0     0 1 0 0 0     0 0 0 0 0
  0 1 4 0 0     0 1 0 5 0     0 0 0 0 0     0 8 0 0 0

Links

Crossrefs

Row 8 of A186851.

Programs

Formula

a(n) = 861896*n^2 - 6840120*n + 12695408 for n >= 12. - Andrew Howroyd, Jan 02 2023

Extensions

Terms a(8) and beyond from Andrew Howroyd, Jan 02 2023
Showing 1-7 of 7 results.

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

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