A389755 Number of (undirected) Hamiltonian paths on the first n cells of the 5 X ceiling(n/5) knight graph.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 95, 144, 82, 16, 125, 1188, 4292, 864, 416, 1030, 28229, 40770, 18784, 3858, 38255, 490809, 2422436, 622868, 274910, 781472, 19903840, 34518608, 18061054, 3321476, 21614495, 275004291, 1129158488, 264895640, 105735266, 308434443, 8657614329, 16039377654

Offset

1,14

Comments

If n is not a multiple of 5, the rightmost column has only n mod 5 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..160

Formula

a(5n) = A083386(n).

Example

For n=14 the a(14)=4 solutions are
 5 14  1
 2  9  4
13  6 11
10  3  8
 7 12    ;
 5 12  1
 2  9  4
13  6 11
10  3  8
 7 14    ;
10  1 14
13  6 11
 2  9  4
 5 12  7
 8  3    ;
 1 12  5
 4  9  2
13  6 11
10  3  8
 7 14    .

Crossrefs

Cf. A083386, A389753, A389754, A389756, A389757, A389758.

Sequence in context: A372821 A151673 A005397 * A259124 A273515 A308225

Adjacent sequences: A389752 A389753 A389754 * A389756 A389757 A389758

Keyword

nonn

Author

Don Knuth, Oct 15 2025

Status

approved