A309271 - OEIS

%I #25 Feb 01 2022 00:29:20

%S 0,0,0,0,0,0,0,0,16,88,464,2076,9904,47456

%N Number of magic knight's tours on a 4 X 2n board.

%D M. Kraitchik, Mathematical Recreations, Dover, 1953, 257-266.

%H G. P. Jelliss, <a href="http://www.mayhematics.com/t/mo.htm">Oblong Magic Knight 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 An example of a magic knight's tour on a 4 X 18 board. All rows sum to 657 and all columns sum to 146:

%e     1 70 33 40  5 42  9 66 29 62 27 58 13 52 25 56 19 50

%e    36 39  4 69 32 65  6 43 10 45 14 61 26 57 20 51 24 55

%e    71  2 37 34 41  8 67 30 63 28 59 12 47 16 53 22 49 18

%e    38 35 72  3 68 31 64  7 44 11 46 15 60 21 48 17 54 23

%Y Cf. A079137, A123936, A309273.

%K nonn,more

%O 1,9

%A _Awani Kumar_, Jul 20 2019