A329370 -id:A329370 - cp's OEIS frontend

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

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

Offset: 1

Awani Kumar, Nov 14 2019

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.

			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

G. P. Jelliss, Quasi-Magic Tours, The Games and Puzzles Journal #26, April-June 2003.
Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Cf. A328816, A329370.

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

Awani Kumar, Dec 17 2019

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.

			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

G. P. Jelliss, Quasi-Magic Tours, The Games and Puzzles Journal #26, April-June 2003.
Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Cf. A328816, A329370, A329483.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs