A330610 Number of near-magic (only short lines are magic) knight's tours on a 4 X 2n board.

0, 0, 0, 4, 16, 72, 244, 1012, 3976, 18440, 81252, 388188, 1800728, 8769964

Offset

1,4

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.

Links

Table of n, a(n) for n=1..14.

G. P. Jelliss, Semi-Magic Knight's Tours.

Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Example

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

Cf. A328816, A329483.

Sequence in context: A124533 A227034 A224660 * A327541 A158784 A180141

Adjacent sequences: A330607 A330608 A330609 * A330611 A330612 A330613

Keyword

nonn,hard,more

Author

Awani Kumar, Dec 20 2019

Status

approved