A330758 Number of quasi-magic (only short lines are magic) knight's tours on a 6 X 2n board.

0, 0, 0, 28, 34, 484

Offset

1,4

Comments

A quasi-magic tour is a special type of semi-magic tour in which the non-magic lines add to only two different 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, Quasi-Magic Tours, The Games and Puzzles Journal #26, April-June 2003.

Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Example

Example of 6 X 10 quasi-magic knight's tour. All short lines add to 183 and the long lines add to either 299 or 311, that is, 305 +- 6.
01 20 59 42 17 26 29 44 15 46
60 41 02 19 28 43 16 47 30 13
21 04 39 58 25 18 27 14 45 48
40 57 22 03 54 51 08 33 12 31
05 38 55 24 07 36 53 10 49 34
56 23 06 37 52 09 50 35 32 11

Crossrefs

Cf. A328872, A329483, A330529.

Sequence in context: A261106 A375819 A138687 * A214470 A055576 A281916

Adjacent sequences: A330755 A330756 A330757 * A330759 A330760 A330761

Keyword

nonn,hard,more

Author

Awani Kumar, Jan 18 2020

Status

approved