A389754 Number of (undirected) Hamiltonian paths on the first n cells of the 4 X ceiling(n/4) knight graph.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 0, 16, 40, 0, 0, 20, 144, 82, 0, 269, 1172, 744, 0, 2643, 13711, 6378, 0, 15192, 72803, 31088, 0, 82790, 440955, 189688, 0, 518913, 2921478, 1213112, 0, 3044484, 17084437, 6683852, 0, 16550347, 96400406, 36486328, 0, 90602461, 550731140, 201282470, 0, 492087597, 3080159951

Offset

1,11

Comments

If n is not a multiple of 4, the rightmost column has only n mod 4 rows (see example).

References

Donald E. Knuth, Hamiltonian paths and cycles, Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).

Links

Don Knuth, Table of n, a(n) for n = 1..128

Formula

a(4*n) = A079137(n).

Example

For n=11, the a(11)=2 solutions are
   1  8  3
   4 11  6
   7  2  9
  10  5    ;
   5  8  3
   2 11  6
   7  4  9
  10  1    .

Crossrefs

Cf. A079137, A389753, A389755, A389756, A389757, A389758.

Sequence in context: A021360 A397191 A382553 * A028256 A209455 A288873

Adjacent sequences: A389751 A389752 A389753 * A389755 A389756 A389757

Keyword

nonn

Author

Don Knuth, Oct 15 2025

Status

approved