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

Author

Awani Kumar, Nov 14 2019

Keywords

• nonn
• hard
• more

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
		

Links

• 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.

Crossrefs

Cf. A328816, A329370.