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 1-3 of 3 results.

A003192 Length of uncrossed knight's path on an n X n board.

Original entry on oeis.org

0, 0, 2, 5, 10, 17, 24, 35, 47
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

I used ZDD techniques to show that a(9)=47. (This is the longest uncrossed knight's path on a 9 X 9 board; thus I confirmed the conjecture that the paths of length 47, found by hand long ago, are indeed optimum.) - Don Knuth, Jun 24 2010
For best known results see link to Alex Chernov's site. - Dmitry Kamenetsky, Mar 02 2021

Examples

			Lengths of longest uncrossed knight's paths on all sufficiently small rectangular boards m X n, with 3 <= m <= n:
......2...4...5...6...8...9..10
..........5...7...9..11..13..15
.............10..14..16..19..22
.................17..21..25..29
.....................24..30..35
.........................35..42
.............................47

References

  • D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, CSLI, Stanford, CA, 2010. (CSLI Lecture Notes, vol. 192)
  • J. S. Madachy, Letter to N. J. A. Sloane, Apr 26 1975.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • Various authors, Uncrossed knight's tours, J. Rec. Math., 2 (1969), 154-157.
  • L. D. Yarbrough, Uncrossed knight's tours, J. Rec. Math., 1 (No. 3, 1969), 140-142.

Links

Crossrefs

Cf. A157416.

Extensions

a(1)=a(2)=0 prepended by Max Alekseyev, Jul 17 2011

A323134 Number of polygons made of uncrossed knight's paths of length 2*n on an infinite board.

Original entry on oeis.org

0, 3, 13, 178, 3031, 64866
Offset: 1

Views

Author

Hugo Pfoertner, Jan 05 2019

Keywords

Examples

			See Pfoertner link.

Links

Crossrefs

Cf. A003192, A157416, A258206, A266549, A284869, A316198.

A072174 Maximum path length of a crippled knight on an n X n board.

Original entry on oeis.org

1, 1, 5, 9, 16, 27, 38, 51, 66
Offset: 1

Views

Author

Jud McCranie, Jun 29 2002

Keywords

Comments

A crippled knight moves one square vertically and two horizontally (or vice versa) and can't land on or pass over any square on which it is previously rested. The initial placement counts as the first move.
a(9) >= 63. - Jud McCranie, May 25 2021
a(9) >= 66. - Giovanni Acerbi, May 20 2024
a(10) >= 79. - Jud McCranie, Aug 17 2025

Examples

			For 3 X 3, the longest path is:
  1 . 3
  4 . .
  . 2 5
The knight cannot move from #5 because it would have to cross over 2 or 3, so a(3)=5.
For 8 X 8, a(8)=51 has a unique solution:
   .  1  8 19 22 25 28 31
   7 20 23 26 29 32  .  .
   2  9 18 21 24 27 30 33
   .  6  3 10 17 34 37 40
   4 11 16 35 38 41  .  .
  49 46  5 12 15 36 39 42
   .  . 50 47 44 13  .  .
  51 48 45 14  .  . 43  .
Best known solution for 9 X 9 (66 moves):
   . 56 53 50 47 44 27  .  .
   .  .  . 55 52 49 46 43 28
  57 54 51 48 45 42 29 26  .
  64 61 58 41 38 35 32  . 30
   .  . 65 62 59 40 37 34 25
  66 63 60 39 36 33 24 31  .
   .  2  5  8 11 14 17 20 23
   4  7 10 13 16 19 22  .  .
   1  .  3  6  9 12 15 18 21

References

  • A crippled knight is defined by Dario Uri in the Journal of Recreational Mathematics, problem 2465, Vol. 29 #4.
  • Vol. 30 #4 has an example for 8 X 8 with 48 moves found by Henry Ibstedt.

Crossrefs

Cf. A003192, A157416, A323131.

Extensions

a(8) by Jud McCranie, Mar 18 2021
a(9) by Jud McCranie, Aug 12 2025
Showing 1-3 of 3 results.

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

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