A330758 -id:A330758 - cp's OEIS frontend

A331483 Number of near-magic (only short lines are magic) knight's tours on a 6 X 2n board.

0, 0, 0, 42, 28, 2056

Offset: 1

Awani Kumar, Jan 18 2020

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.

			Example of 6 X 10 near-magic knight's tour. All short lines add to 183 and the long lines add to the magic constant 305 and 305 +- 6.
29 50 53 14 27 16 55 38 03 20
52 13 28 17 54 25 02 19 56 39
49 30 51 26 15 18 37 60 21 04
12 09 32 45 36 43 24 01 40 57
31 48 11 34 07 46 59 42 05 22
10 33 08 47 44 35 06 23 58 41

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

Cf. A330610, A330758.

cp's OEIS Frontend

A331483 Number of near-magic (only short lines are magic) knight's tours on a 6 X 2n board.

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