A389756 Number of (undirected) Hamiltonian paths on the first n cells of the 6 X ceiling(n/6) knight graph.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 1286, 1172, 744, 207, 800, 4607, 60293, 40770, 18784, 9133, 44778, 247872, 4453920, 3354758, 3318960, 1321288, 6063880, 27757719, 465898661, 415326332, 389969466, 136305454, 544834030, 2358474638, 38575344556, 28472206621, 24964893804

Offset

1,21

Comments

If n is not a multiple of 6, the rightmost column has only n mod 6 rows.

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..192

Formula

a(6n) = A306281(n).

Crossrefs

Cf. A306281, A389753, A389754, A389755, A389757, A389758.

Sequence in context: A093982 A091548 A342899 * A017769 A017716 A180365

Adjacent sequences: A389753 A389754 A389755 * A389757 A389758 A389759

Keyword

nonn

Author

Don Knuth, Oct 15 2025

Status

approved