A123935 -id:A123935 - cp's OEIS frontend

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

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

Eric W. Weisstein, Dec 28 2002

nonn

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

Andrew Howroyd, Table of n, a(n) for n = 1..500
George Jellis, Knight's tour diagrams
Colin Rose, Knight's tours
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Knight Graph

See A079312 for 4 times these numbers, A123935 for twice these numbers, A123936 for these numbers halved.

Cf. A169696, A083386, A165134, A328341.

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

N. J. A. Sloane, Oct 30 2006

nonn

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

Andrew Howroyd, Table of n, a(n) for n = 1..500

Cf. A079137, A123935, A328341.

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

A306282 Triangle read by rows: T(n,k) is the number of (directed) Hamiltonian paths in the n X k knight graph.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 164, 1728, 0, 0, 0, 1488, 37568, 6637920, 0, 0, 104, 12756, 1245736, 779938932, 165575218320, 0, 0, 792, 62176, 36122108

Offset: 1

Seiichi Manyama, Feb 03 2019

			Triangle begins:
n\k | 1  2    3      4        5          6             7
----+----------------------------------------------------
1   | 1;
2   | 0, 0;
3   | 0, 0,   0;
4   | 0, 0,  16,     0;
5   | 0, 0,   0,   164,    1728;
6   | 0, 0,   0,  1488,   37568,   6637920;
7   | 0, 0, 104, 12756, 1245736, 779938932, 165575218320;

Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Knight Graph

T(n,n) gives A165134.

Cf. A118067, A123935.

cp's OEIS Frontend

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

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

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A306282 Triangle read by rows: T(n,k) is the number of (directed) Hamiltonian paths in the n X k knight graph.

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