A389757 Number of (undirected) Hamiltonian paths on the first n cells of the 7 X ceiling(n/7) knight graph.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 44, 52, 160, 239, 1595, 1391, 13438, 13711, 6378, 1930, 11394, 48948, 312319, 1151375, 2422436, 622868, 577180, 1063017, 11791551, 34929196, 398826652, 415326332, 389969466, 169379360, 877515711, 3233718689, 20262979397, 79131917546, 265583249088

Offset

1,19

Comments

If n is not a multiple of 7, the rightmost column has only n mod 7 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..224

Formula

a(7n) = A306283(n).

Crossrefs

Cf. A306283, A389753, A389754, A389756, A389758.

Sequence in context: A364680 A284065 A063837 * A392563 A344871 A071125

Adjacent sequences: A389754 A389755 A389756 * A389758 A389759 A389760

Keyword

nonn

Author

Don Knuth, Oct 15 2025

Status

approved