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

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

Offset

1,7

Links

Table of n, a(n) for n=1..22.

G. P. Jelliss, Semi-magic Knight's Tours

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

Example

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

Crossrefs

Cf. A079137, A123936, A309271.

Sequence in context: A134937 A076431 A221856 * A358627 A282470 A067956

Adjacent sequences: A309270 A309271 A309272 * A309274 A309275 A309276

Keyword

nonn,more

Author

Awani Kumar, Jul 20 2019

Status

approved