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A330611 Number of near-magic (only long lines are magic) knight's tours on a 4 X 2n board. 0
0, 0, 2, 16, 22, 112, 330, 1304, 6322 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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 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
CROSSREFS
Sequence in context: A118954 A119599 A333475 * A228158 A330662 A337426
KEYWORD
nonn,hard,more
AUTHOR
Awani Kumar, Dec 20 2019
STATUS
approved

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)