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 1-5 of 5 results.

A329483 Number of quasi-magic (only short lines are magic) knight's tours on a 4 X 2n board.

Original entry on oeis.org

0, 0, 0, 4, 12, 28, 136, 488, 2624, 12420, 64120, 313584, 1675648, 8536072
Offset: 1

Views

Author

Awani Kumar, Nov 14 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 short lines sum to 114 and the long lines sum to 397 and 401, that is, 399 +- 2.
   3 56 25 32  5 52 21 36  9 48 11 40 15 44
  26 29  4 53 24 33  8 49 20 37 18 43 12 41
  55  2 31 28 51  6 35 22 47 10 39 14 45 16
  30 27 54  1 34 23 50  7 38 19 46 17 42 13
		

Crossrefs

A329370 Number of semi-magic (only long lines are magic) knight's tours on a 4 X 2n board.

Original entry on oeis.org

0, 0, 16, 136, 3102, 58356, 1092618
Offset: 1

Views

Author

Awani Kumar, Nov 12 2019

Keywords

Examples

			Example 4 X 10 semi-magic knight's tour (only long lines are magic, Magic Constant is 205):
   1 22  3 40 17 34  9 30 13 36
   4 25 20 27  8 29 16 35 10 31
  21  2 23  6 39 18 33 12 37 14
  24  5 26 19 28  7 38 15 32 11
		

Crossrefs

Cf. A328816.

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

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 1-5 of 5 results.