A330610 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.