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

0, 0, 2, 16, 22, 112, 330, 1304, 6322

Offset: 1

Author

Awani Kumar, Dec 20 2019

Keywords

• nonn
• hard
• more

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
		

Links

• G. P. Jelliss, Semi-Magic Knight's Tours.
• Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Crossrefs

Cf. A328816, A329483, A330610.