A329483
Number of quasi-magic (only short lines are magic) knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 0, 4, 12, 28, 136, 488, 2624, 12420, 64120, 313584, 1675648, 8536072
Offset: 1
Example of 4 X 14 quasi-magic knight's tour. All short lines sum to 114 and the long lines sum to 397 and 401, that is, 399 +- 2.
3 56 25 32 5 52 21 36 9 48 11 40 15 44
26 29 4 53 24 33 8 49 20 37 18 43 12 41
55 2 31 28 51 6 35 22 47 10 39 14 45 16
30 27 54 1 34 23 50 7 38 19 46 17 42 13
A329370
Number of semi-magic (only long lines are magic) knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 16, 136, 3102, 58356, 1092618
Offset: 1
Example 4 X 10 semi-magic knight's tour (only long lines are magic, Magic Constant is 205):
1 22 3 40 17 34 9 30 13 36
4 25 20 27 8 29 16 35 10 31
21 2 23 6 39 18 33 12 37 14
24 5 26 19 28 7 38 15 32 11
A330610
Number of near-magic (only short lines are magic) knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 0, 4, 16, 72, 244, 1012, 3976, 18440, 81252, 388188, 1800728, 8769964
Offset: 1
Example of 4 X 14 near-magic knight's tour. All short lines add to 114 and the long lines add to the magic constant 399 and 399 +- 4.
1 54 25 32 5 36 23 50 19 44 9 40 15 46
28 31 4 53 24 51 20 35 8 39 14 45 10 41
55 2 29 26 33 6 37 22 49 18 43 12 47 16
30 27 56 3 52 21 34 7 38 13 48 17 42 11
A330529
Number of quasi-magic (only long lines are magic) knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 4, 10, 30, 48, 170, 710, 2492
Offset: 1
Example of 4 X 14 quasi-magic knight's tour. All long lines sum to 399 and the short lines sum to either 112 or 126.
3 52 19 40 1 50 21 42 13 48 23 30 11 46
18 39 2 51 20 41 14 49 22 29 12 47 24 31
53 4 37 16 55 6 35 28 43 8 33 26 45 10
38 17 54 5 36 15 56 7 34 27 44 9 32 25
A330611
Number of near-magic (only long lines are magic) knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 2, 16, 22, 112, 330, 1304, 6322
Offset: 1
Example of 4 x 14 near-magic knight's tour. All long lines add to 399 and the short lines add to the magic constant 114 and 114 +- 4.
1 54 25 32 5 52 23 48 9 38 11 40 17 44
28 31 4 53 24 33 6 37 20 47 18 43 14 41
55 2 29 26 51 22 35 8 49 10 39 12 45 16
30 27 56 3 34 7 50 21 36 19 46 15 42 13
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