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 1-4 of 4 results.

A330610 Number of near-magic (only short lines are magic) knight's tours on a 4 X 2n board.

Original entry on oeis.org

0, 0, 0, 4, 16, 72, 244, 1012, 3976, 18440, 81252, 388188, 1800728, 8769964
Offset: 1

Views

Author

Awani Kumar, Dec 20 2019

Keywords

Comments

A semi-magic knight's tour is a tour that adds to a constant sum in every line in one direction, but not in every line in the perpendicular direction. A near-magic tour is a special type of semi-magic tour in which the non-magic direction has the lines add to the magic constant and two other values. Such tours are of interest on boards where magic tours don't exist.

Examples

			Example of 4 X 14 near-magic knight's tour. All short lines add to 114 and the long lines add to the magic constant 399 and 399 +- 4.
   1 54 25 32  5 36 23 50 19 44  9 40 15 46
  28 31  4 53 24 51 20 35  8 39 14 45 10 41
  55  2 29 26 33  6 37 22 49 18 43 12 47 16
  30 27 56  3 52 21 34  7 38 13 48 17 42 11
		

Crossrefs

A330529 Number of quasi-magic (only long lines are magic) knight's tours on a 4 X 2n board.

Original entry on oeis.org

0, 0, 4, 10, 30, 48, 170, 710, 2492
Offset: 1

Views

Author

Awani Kumar, Dec 17 2019

Keywords

Comments

A quasi-magic tour is a special type of semi-magic tour in which the non-magic lines add to only two different values. Such tours are of interest on boards where magic tours don't exist.

Examples

			Example of 4 X 14 quasi-magic knight's tour. All long lines sum to 399 and the short lines sum to either 112 or 126.
   3 52 19 40  1 50 21 42 13 48 23 30 11 46
  18 39  2 51 20 41 14 49 22 29 12 47 24 31
  53  4 37 16 55  6 35 28 43  8 33 26 45 10
  38 17 54  5 36 15 56  7 34 27 44  9 32 25
		

Crossrefs

A330758 Number of quasi-magic (only short lines are magic) knight's tours on a 6 X 2n board.

Original entry on oeis.org

0, 0, 0, 28, 34, 484
Offset: 1

Views

Author

Awani Kumar, Jan 18 2020

Keywords

Comments

A quasi-magic tour is a special type of semi-magic tour in which the non-magic lines add to only two different values. Such tours are of interest on boards where magic tours don't exist.

Examples

			Example of 6 X 10 quasi-magic knight's tour. All short lines add to 183 and the long lines add to either 299 or 311, that is, 305 +- 6.
01 20 59 42 17 26 29 44 15 46
60 41 02 19 28 43 16 47 30 13
21 04 39 58 25 18 27 14 45 48
40 57 22 03 54 51 08 33 12 31
05 38 55 24 07 36 53 10 49 34
56 23 06 37 52 09 50 35 32 11
		

Crossrefs

A330611 Number of near-magic (only long lines are magic) knight's tours on a 4 X 2n board.

Original entry on oeis.org

0, 0, 2, 16, 22, 112, 330, 1304, 6322
Offset: 1

Views

Author

Awani Kumar, Dec 20 2019

Keywords

Comments

A semi-magic knight's tour is a tour that adds to a constant sum in every line in one direction, but not in every line in the perpendicular direction. A near-magic tour is a special type of semi-magic tour in which the non-magic direction has the lines add to the magic constant and two other values. Such tours are of interest on boards where magic tours don't exist.

Examples

			Example of 4 x 14 near-magic knight's tour. All long lines add to 399 and the short lines add to the magic constant 114 and 114 +- 4.
   1 54 25 32  5 52 23 48  9 38 11 40 17 44
  28 31  4 53 24 33  6 37 20 47 18 43 14 41
  55  2 29 26 51 22 35  8 49 10 39 12 45 16
  30 27 56  3 34  7 50 21 36 19 46 15 42 13
		

Crossrefs

Showing 1-4 of 4 results.