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

1,4

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..6.

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 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

Crossrefs

Cf. A330610, A330758.

Sequence in context: A236684 A053721 A195750 * A342151 A070723 A221213

Adjacent sequences: A331480 A331481 A331482 * A331484 A331485 A331486

Keyword

nonn,hard,more

Author

Awani Kumar, Jan 18 2020

Status

approved