A389759 - OEIS

A389759

Number of (undirected) Hamiltonian paths on the first n cells of the 3 X ceiling(n/3) knight graph.

1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 8, 8, 4, 0, 8, 0, 0, 20, 44, 52, 465, 276, 396, 988, 824, 560, 3888, 1384, 3048, 10348, 12796, 10672, 69831, 36962, 57248, 171104, 155756, 128864, 815520, 405024, 646272, 2219336, 2132304, 1838784, 11184337, 6011834, 8636880, 30354388, 26341332, 23400992, 138689004, 75211944

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OFFSET

1,10

COMMENTS

If n is not a multiple of 3, the righthand column has only n mod 3 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..297

FORMULA

a(3*n) = A169696(n).

EXAMPLE

For n=10, the a(10)=2 solutions are

7 4 9 2

10 1 6

5 8 3 ;

7 10 5 2

4 1 8

9 6 3 .

CROSSREFS

Cf. A169696, A389754, A389755, A389756, A389757, A389758.

Sequence in context: A021441 A196066 A334574 * A260825 A330763 A138102

Adjacent sequences: A389756 A389757 A389758 * A389760 A389761 A389762

KEYWORD

nonn

AUTHOR

Don Knuth, Oct 15 2025

STATUS

approved