A328341 Number of geometrically distinct open knight's tours on a 4 X n chessboard.

0, 0, 3, 0, 22, 186, 1603, 7772, 47478, 303278, 1671273, 9121582, 50322028, 270896326, 1426536267, 7454807822, 38607660199, 197696949844, 1003736587788, 5060326202622, 25334034892953, 126024078250318, 623383415637750, 3067618264121349, 15022847233751804, 73245459228339114

Offset

1,3

Links

Table of n, a(n) for n=1..26.

George Jellis, Knight's tours of Four Rank Boards

Formula

a(2*n) = A123936(2*n)/2; a(2*n-1) = (A123936(2*n-1) + A328340(n))/2.

Example

a(3) = 3 because there are two symmetric and one asymmetric tour:
  +----+----+----+----+   +----+----+----+----+   +----+----+----+----+
  |  8 | 11 |  6 |  3 |   |  1 |  4 |  7 | 10 |   |  1 |  4 |  7 | 10 |
  +----+----+----+----+   +----+----+----+----+   +----+----+----+----+
  |  1 |  4 |  9 | 12 |   |  8 | 11 |  2 |  5 |   | 12 |  9 |  2 |  5 |
  +----+----+----+----+   +----+----+----+----+   +----+----+----+----+
  | 10 |  7 |  2 |  5 |   |  3 |  6 |  9 | 12 |   |  3 |  6 | 11 |  8 |
  +----+----+----+----+   +----+----+----+----+   +----+----+----+----+

Crossrefs

Cf. A079137, A123936, A169777, A328340.

Sequence in context: A083289 A108196 A370015 * A013460 A013388 A344996

Adjacent sequences: A328338 A328339 A328340 * A328342 A328343 A328344

Keyword

nonn

Author

Andrew Howroyd, Oct 12 2019

Status

approved