A328340 Number of geometrically distinct symmetric open knight's tours on a 4 X (2n-1) chessboard.

0, 2, 3, 17, 112, 620, 2821, 13805, 69036, 327978, 1540792, 7274254, 34083946, 158284977, 732296355, 3377163866, 15513066609, 71017218563, 324217343701, 1476439351581, 6707726917103, 30409720266127, 137599767926968, 621531352302268, 2802892252591572, 12621236296192889

Offset: 1

Author

Andrew Howroyd, Oct 12 2019

Keywords

• nonn

Comments

Symmetric tours are only possible on boards of odd length. The only symmetry is a rotation by 180 degrees which results in the reversal of the tour.

Examples

			a(2) = 2 because there are 2 symmetric 4 X 3 tours:
  +----+----+----+----+   +----+----+----+----+
  |  8 | 11 |  6 |  3 |   |  1 |  4 |  7 | 10 |
  +----+----+----+----+   +----+----+----+----+
  |  1 |  4 |  9 | 12 |   |  8 | 11 |  2 |  5 |
  +----+----+----+----+   +----+----+----+----+
  | 10 |  7 |  2 |  5 |   |  3 |  6 |  9 | 12 |
  +----+----+----+----+   +----+----+----+----+
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..250
• George Jellis, Knight's tours of Four Rank Boards

Crossrefs

Cf. A079137, A328341.