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A330610
Number of near-magic (only short lines are magic) knight's tours on a 4 X 2n board.
2
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
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
Sequence in context: A124533 A227034 A224660 * A327541 A158784 A180141
KEYWORD
nonn,hard,more
AUTHOR
Awani Kumar, Dec 20 2019
STATUS
approved