cp's OEIS Frontend

A309273 Number of semi-magic (only short lines are magic) knight's tours on a 4 X n board.

%I A309273 #14 Feb 01 2022 00:29:34
%S A309273 0,0,0,0,0,0,9,16,38,104,267,608,1444,3480,8221,19212,45262,213280,
%T A309273 250247,587072,1378912,3237456
%N A309273 Number of semi-magic (only short lines are magic) knight's tours on a 4 X n board.
%H A309273 G. P. Jelliss, <a href="https://www.mayhematics.com/t/mk1.htm">Semi-magic Knight's Tours</a>
%H A309273 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 A309273 Example 4 X 7 semi-magic knight's tour (only short lines are magic):
%e A309273   +----+----+----+----+----+----+----+
%e A309273   |  9 | 28 |  7 | 18 |  3 | 24 | 13 |
%e A309273   +----+----+----+----+----+----+----+
%e A309273   |  6 | 17 | 10 | 25 | 14 | 21 |  2 |
%e A309273   +----+----+----+----+----+----+----+
%e A309273   | 27 |  8 | 15 |  4 | 19 | 12 | 23 |
%e A309273   +----+----+----+----+----+----+----+
%e A309273   | 16 |  5 | 26 | 11 | 22 |  1 | 20 |
%e A309273   +----+----+----+----+----+----+----+
%e A309273 .
%e A309273 Example 4 X 16 semi-magic knight's tour (only short lines are magic):
%e A309273    1 62  3 36 29 38 19 58 25 44 17 56 23 52 15 54
%e A309273   32 35 30 61  4 59 26 45 18 57 24 43 16 55 12 51
%e A309273   63  2 33 28 37  6 39 20 47  8 41 22 49 10 53 14
%e A309273   34 31 64  5 60 27 46  7 40 21 48  9 42 13 50 11
%Y A309273 Cf. A079137, A123936, A309271.
%K A309273 nonn,more
%O A309273 1,7
%A A309273 _Awani Kumar_, Jul 20 2019