Awani Kumar has authored 11 sequences. Here are the ten most recent ones:
A331483
Number of near-magic (only short lines are magic) knight's tours on a 6 X 2n board.
Original entry on oeis.org
0, 0, 0, 42, 28, 2056
Offset: 1
Example of 6 X 10 near-magic knight's tour. All short lines add to 183 and the long lines add to the magic constant 305 and 305 +- 6.
29 50 53 14 27 16 55 38 03 20
52 13 28 17 54 25 02 19 56 39
49 30 51 26 15 18 37 60 21 04
12 09 32 45 36 43 24 01 40 57
31 48 11 34 07 46 59 42 05 22
10 33 08 47 44 35 06 23 58 41
A330758
Number of quasi-magic (only short lines are magic) knight's tours on a 6 X 2n board.
Original entry on oeis.org
0, 0, 0, 28, 34, 484
Offset: 1
Example of 6 X 10 quasi-magic knight's tour. All short lines add to 183 and the long lines add to either 299 or 311, that is, 305 +- 6.
01 20 59 42 17 26 29 44 15 46
60 41 02 19 28 43 16 47 30 13
21 04 39 58 25 18 27 14 45 48
40 57 22 03 54 51 08 33 12 31
05 38 55 24 07 36 53 10 49 34
56 23 06 37 52 09 50 35 32 11
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
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
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
A328872
Number of semi-magic (only short lines are magic) knight's tours on a 6 X n board.
Original entry on oeis.org
0, 0, 0, 0, 0, 88, 288, 1880, 9994, 93718, 660282, 4310970
Offset: 1
Example 6 X 7 semi-magic knight's tour (only short lines are magic):
+----+----+----+----+----+----+----+
| 1 | 28 | 3 | 6 | 31 | 26 | 23 |
+----+----+----+----+----+----+----+
| 4 | 7 | 30 | 27 | 24 | 19 | 32 |
+----+----+----+----+----+----+----+
| 29 | 2 | 5 | 8 | 33 | 22 | 25 |
+----+----+----+----+----+----+----+
| 14 | 41 | 38 | 35 | 20 | 11 | 18 |
+----+----+----+----+----+----+----+
| 39 | 36 | 13 | 16 | 9 | 34 | 21 |
+----+----+----+----+----+----+----+
| 42 | 15 | 40 | 37 | 12 | 17 | 10 |
+----+----+----+----+----+----+----+
A328816
Number of semi-magic (only short lines are magic) knight's tours on a 4 X 2n board.
Original entry on oeis.org
0, 0, 0, 16, 104, 608, 3480, 19212, 213280, 587072, 3237456
Offset: 1
Example of a 4 X 10 semi-magic knight's tour (only the short lines are magic):
+----+----+----+----+----+----+----+----+----+----+
| 1 | 38 | 3 | 24 | 5 | 34 | 9 | 26 | 13 | 30 |
+----+----+----+----+----+----+----+----+----+----+
| 20 | 23 | 18 | 37 | 8 | 25 | 6 | 29 | 10 | 27 |
+----+----+----+----+----+----+----+----+----+----+
| 39 | 2 | 21 | 4 | 33 | 16 | 35 | 12 | 31 | 14 |
+----+----+----+----+----+----+----+----+----+----+
| 22 | 19 | 40 | 17 | 36 | 7 | 32 | 15 | 28 | 11 |
+----+----+----+----+----+----+----+----+----+----+
A309273
Number of semi-magic (only short lines are magic) knight's tours on a 4 X n board.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 9, 16, 38, 104, 267, 608, 1444, 3480, 8221, 19212, 45262, 213280, 250247, 587072, 1378912, 3237456
Offset: 1
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
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