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%I #6 Jan 14 2020 01:03:04
%S 0,0,2,16,22,112,330,1304,6322
%N Number of near-magic (only long lines are magic) knight's tours on a 4 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 4 x 14 near-magic knight's tour. All long lines add to 399 and the short lines add to the magic constant 114 and 114 +- 4.
%e 1 54 25 32 5 52 23 48 9 38 11 40 17 44
%e 28 31 4 53 24 33 6 37 20 47 18 43 14 41
%e 55 2 29 26 51 22 35 8 49 10 39 12 45 16
%e 30 27 56 3 34 7 50 21 36 19 46 15 42 13
%Y Cf. A328816, A329483, A330610.
%K nonn,hard,more
%O 1,3
%A _Awani Kumar_, Dec 20 2019
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