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%I #25 Jan 18 2020 13:24:48
%S 0,0,0,28,34,484
%N Number of quasi-magic (only short lines are magic) knight's tours on a 6 X 2n board.
%C 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.
%H G. P. Jelliss, <a href="https://www.mayhematics.com/j/gpj26.htm">Quasi-Magic Tours</a>, The Games and Puzzles Journal #26, April-June 2003.
%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 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.
%e 01 20 59 42 17 26 29 44 15 46
%e 60 41 02 19 28 43 16 47 30 13
%e 21 04 39 58 25 18 27 14 45 48
%e 40 57 22 03 54 51 08 33 12 31
%e 05 38 55 24 07 36 53 10 49 34
%e 56 23 06 37 52 09 50 35 32 11
%Y Cf. A328872, A329483, A330529.
%K nonn,hard,more
%O 1,4
%A _Awani Kumar_, Jan 18 2020