A394066 Number of directed paths in the n X n grid graph, reduced for symmetry (with rotations, reflections, and translations not counted as distinct).

0, 3, 60, 2835, 330598, 99784390, 81407472923

Offset

1,2

Comments

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

Number of undirected paths gives A394065. Number of directed paths not reduced for symmetry gives A288032*2.

Links

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

Example

a(2) = 3 (all symmetric and count as 1 each both undirected and directed):
  +  +    +>>+    +>>+
             v       v
  +>>+    +  +    +<<+.
Nonsymmetric paths count as 2 each when directed, e.g.:
  +  +--+      +  +>>+       +  +<<+
        |            v             ^
  +  +  +  ->  +  +  +  and  +  +  +
        |            v             ^
  +  +  +      +  +  +       +  +  +.

Prog

(PARI) \\ See Hohn link in A394065.

Crossrefs

Cf. A394065, A288032.

Sequence in context: A081854 A085990 A202065 * A394531 A036770 A201699

Adjacent sequences: A394063 A394064 A394065 * A394067 A394068 A394069

Keyword

nonn,more

Author

Charles L. Hohn, Mar 09 2026

Status

approved