A309271 -id:A309271 - cp's OEIS frontend

A328816 Number of semi-magic (only short lines are magic) knight's tours on a 4 X 2n board.

0, 0, 0, 16, 104, 608, 3480, 19212, 213280, 587072, 3237456

Offset: 1

Awani Kumar, Oct 28 2019

			Example of a 4 X 10 semi-magic knight's tour (only the short lines are magic):
   +----+----+----+----+----+----+----+----+----+----+
   |  1 | 38 |  3 | 24 |  5 | 34 |  9 | 26 | 13 | 30 |
   +----+----+----+----+----+----+----+----+----+----+
   | 20 | 23 | 18 | 37 |  8 | 25 |  6 | 29 | 10 | 27 |
   +----+----+----+----+----+----+----+----+----+----+
   | 39 |  2 | 21 |  4 | 33 | 16 | 35 | 12 | 31 | 14 |
   +----+----+----+----+----+----+----+----+----+----+
   | 22 | 19 | 40 | 17 | 36 |  7 | 32 | 15 | 28 | 11 |
   +----+----+----+----+----+----+----+----+----+----+

G. P. Jelliss, Oblong Magic Knight Tours
Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Cf. A309273, A309271.

a(n) = A309273(2*n).

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

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 9, 16, 38, 104, 267, 608, 1444, 3480, 8221, 19212, 45262, 213280, 250247, 587072, 1378912, 3237456

Offset: 1

Awani Kumar, Jul 20 2019

			Example 4 X 7 semi-magic knight's tour (only short lines are magic):
  +----+----+----+----+----+----+----+
  |  9 | 28 |  7 | 18 |  3 | 24 | 13 |
  +----+----+----+----+----+----+----+
  |  6 | 17 | 10 | 25 | 14 | 21 |  2 |
  +----+----+----+----+----+----+----+
  | 27 |  8 | 15 |  4 | 19 | 12 | 23 |
  +----+----+----+----+----+----+----+
  | 16 |  5 | 26 | 11 | 22 |  1 | 20 |
  +----+----+----+----+----+----+----+
.
Example 4 X 16 semi-magic knight's tour (only short lines are magic):
   1 62  3 36 29 38 19 58 25 44 17 56 23 52 15 54
  32 35 30 61  4 59 26 45 18 57 24 43 16 55 12 51
  63  2 33 28 37  6 39 20 47  8 41 22 49 10 53 14
  34 31 64  5 60 27 46  7 40 21 48  9 42 13 50 11

G. P. Jelliss, Semi-magic Knight's Tours
Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

Cf. A079137, A123936, A309271.

cp's OEIS Frontend

A328816 Number of semi-magic (only short lines are magic) knight's tours on a 4 X 2n board.

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