login
A328340
Number of geometrically distinct symmetric open knight's tours on a 4 X (2n-1) chessboard.
2
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
1,2
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.
EXAMPLE
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 |
+----+----+----+----+ +----+----+----+----+
CROSSREFS
Sequence in context: A056794 A135726 A259535 * A042978 A089675 A041383
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 12 2019
STATUS
approved