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.

Showing 1-3 of 3 results.

A079137 Number of (undirected) Hamiltonian paths on the 4 X n knight graph.

Original entry on oeis.org

0, 0, 8, 0, 82, 744, 6378, 31088, 189688, 1213112, 6683852, 36486328, 201282470, 1083585304, 5706117458, 29819231288, 154430502724, 790787799376, 4014945695196, 20241304810488, 101336136490228, 504096313001272, 2493533648002492, 12270473056485396
Offset: 1

Views

Author

Eric W. Weisstein, Dec 28 2002

Keywords

References

  • Kraitchik, M. Mathematical Recreations. New York: W. W. Norton, p. 263, 1942.

Links

Crossrefs

See A079312 for 4 times these numbers, A123935 for twice these numbers, A123936 for these numbers halved.
Cf. A169696, A083386, A165134, A328341.

Extensions

More terms from André Pönitz (poenitz(AT)htwm.de), Jun 11 2003
Edited by N. J. A. Sloane, Oct 30 2006, following suggestions from Colin Rose
Terms a(22) and beyond from Andrew Howroyd, Jul 01 2017

A123936 a(n) = A079137(n)/2.

Original entry on oeis.org

0, 0, 4, 0, 41, 372, 3189, 15544, 94844, 606556, 3341926, 18243164, 100641235, 541792652, 2853058729, 14909615644, 77215251362, 395393899688, 2007472847598, 10120652405244, 50668068245114, 252048156500636, 1246766824001246, 6135236528242698, 30045694433419662
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2006

Keywords

Comments

Number of nonequivalent (or geometrically distinct) directed open knight's tours on a 4 X n chessboard up to rotation and reflection. See A328341 for the number of geometrically distinct undirected open knights's tours. - Andrew Howroyd, Oct 12 2019

Links

Crossrefs

Cf. A079137, A123935, A328341.

Extensions

Terms a(22) and beyond from Andrew Howroyd, Oct 13 2019

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

Links

Crossrefs

Cf. A079137, A328341.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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