A331483 - OEIS

%I #6 Jan 19 2020 11:33:34

%S 0,0,0,42,28,2056

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

%C 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.

%H G. P. Jelliss, <a href="https://www.mayhematics.com/t/mk.htm">Semi-Magic Knight's Tours</a>.

%H Awani Kumar, <a href="https://arxiv.org/abs/1802.09340">Studies in Tours of Knight on Rectangular Boards</a>, arXiv:1802.09340 [math.GM], 2018.

%e 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.

%e 29 50 53 14 27 16 55 38 03 20

%e 52 13 28 17 54 25 02 19 56 39

%e 49 30 51 26 15 18 37 60 21 04

%e 12 09 32 45 36 43 24 01 40 57

%e 31 48 11 34 07 46 59 42 05 22

%e 10 33 08 47 44 35 06 23 58 41

%Y Cf. A330610, A330758.

%K nonn,hard,more

%O 1,4

%A _Awani Kumar_, Jan 18 2020