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

0, 0, 4, 10, 30, 48, 170, 710, 2492

Offset: 1

Author

Awani Kumar, Dec 17 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 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
		

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, A329483.