A394067 Number of undirected cycles in the n X n grid graph, reduced for symmetry (with rotations, reflections, and translations not counted as distinct).

0, 1, 4, 33, 1005, 134899, 56447000

Offset

1,3

Comments

Excludes 0 length cycles; including them increases each term by 1.

Number of directed cycles gives A390122. Number of undirected cycles not reduced for symmetry gives A140517.

Links

Table of n, a(n) for n=1..7.

Example

a(3) = 4:
  +--+--+    +  +  +    +  +  +    +--+--+
  |     |                          |     |
  +  +  +    +--+--+    +  +--+    +--+  +
  |     |    |     |       |  |       |  |
  +--+--+    +--+--+    +  +--+    +  +--+.

Prog

(PARI) \\ See Hohn link in A394065.

Crossrefs

Cf. A390122, A140517.

Sequence in context: A113086 A058153 A382018 * A020197 A102959 A057959

Adjacent sequences: A394064 A394065 A394066 * A394068 A394069 A394071

Keyword

nonn,more

Author

Charles L. Hohn, Mar 09 2026

Status

approved