A397797 Number of free ouroboros polyknights with 2*n cells.

0, 3, 16, 157, 1707, 25889

Offset

1,2

Comments

In analogy with the definition in A359706, an ouroboros polyknight is a polyknight in which every cell has exactly two neighbors.

There are no ouroboros polyknights with an odd number of cells.

Equivalently, a(n) is the number of induced cycles of length 2*n in the infinite knight graph, up to translations, rotations, and reflections.

Links

Table of n, a(n) for n=1..6.

Pontus von Brömssen, Illustration of all ouroboros polyknights with at most 6 cells.

Index entries for sequences related to polyominoes.

Crossrefs

Cf. A030446, A165143, A297666, A359706.

Sequence in context: A229954 A228513 A135753 * A191959 A349591 A091146

Adjacent sequences: A397794 A397795 A397796 * A397798 A397799 A397800

Keyword

nonn,hard,more,new

Author

Pontus von Brömssen, Jul 12 2026

Status

approved