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%I #14 Feb 01 2022 00:29:34
%S 0,0,0,0,0,0,9,16,38,104,267,608,1444,3480,8221,19212,45262,213280,
%T 250247,587072,1378912,3237456
%N Number of semi-magic (only short lines are magic) knight's tours on a 4 X n board.
%H G. P. Jelliss, <a href="https://www.mayhematics.com/t/mk1.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 4 X 7 semi-magic knight's tour (only short lines are magic):
%e +----+----+----+----+----+----+----+
%e | 9 | 28 | 7 | 18 | 3 | 24 | 13 |
%e +----+----+----+----+----+----+----+
%e | 6 | 17 | 10 | 25 | 14 | 21 | 2 |
%e +----+----+----+----+----+----+----+
%e | 27 | 8 | 15 | 4 | 19 | 12 | 23 |
%e +----+----+----+----+----+----+----+
%e | 16 | 5 | 26 | 11 | 22 | 1 | 20 |
%e +----+----+----+----+----+----+----+
%e .
%e Example 4 X 16 semi-magic knight's tour (only short lines are magic):
%e 1 62 3 36 29 38 19 58 25 44 17 56 23 52 15 54
%e 32 35 30 61 4 59 26 45 18 57 24 43 16 55 12 51
%e 63 2 33 28 37 6 39 20 47 8 41 22 49 10 53 14
%e 34 31 64 5 60 27 46 7 40 21 48 9 42 13 50 11
%Y Cf. A079137, A123936, A309271.
%K nonn,more
%O 1,7
%A _Awani Kumar_, Jul 20 2019