cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-13 of 13 results.

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

Views

Author

Eric W. Weisstein, May 14 2019

Keywords

Crossrefs

Cf. A165134, A169696 (3 X n), A079137 (4 X n), A083386 (5 X n), A306281 (6 X n), A306283 (7 X n).

Formula

a(n) = A165134(n)/2.

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

Views

Author

Awani Kumar, Jul 20 2019

Keywords

Examples

			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
		

References

  • M. Kraitchik, Mathematical Recreations, Dover, 1953, 257-266.

Crossrefs

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

Views

Author

Andrew Howroyd, Oct 12 2019

Keywords

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 |
  +----+----+----+----+   +----+----+----+----+
		

Crossrefs

Previous Showing 11-13 of 13 results.