A308131
Number of (undirected) Hamiltonian paths in the n X n knight graph.
Original entry on oeis.org
0, 0, 0, 0, 864, 3318960, 82787609160, 9795914085489952
Offset: 1
A309271
Number of magic knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 16, 88, 464, 2076, 9904, 47456
Offset: 1
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:
1 70 33 40 5 42 9 66 29 62 27 58 13 52 25 56 19 50
36 39 4 69 32 65 6 43 10 45 14 61 26 57 20 51 24 55
71 2 37 34 41 8 67 30 63 28 59 12 47 16 53 22 49 18
38 35 72 3 68 31 64 7 44 11 46 15 60 21 48 17 54 23
- M. Kraitchik, Mathematical Recreations, Dover, 1953, 257-266.
A328340
Number of geometrically distinct symmetric open knight's tours on a 4 X (2n-1) chessboard.
Original entry on oeis.org
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
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 |
+----+----+----+----+ +----+----+----+----+
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