A324603 Number of non-intersecting loops starting at (0,0) on the n X n torus consisting of steps up and to the right.

2, 4, 22, 258, 3528, 87830, 8295536

Offset

1,1

Links

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

Peter Kagey, Cycles on the torus, Programming Puzzles & Code Golf Stack Exchange.

Example

On the 2 X 2 torus, the 4 walks are:
  [(0,0),(1,0),(0,0)]
  [(0,0),(0,1),(0,0)]
  [(0,0),(0,1),(1,1),(1,0),(0,0)]
  [(0,0),(1,0),(1,1),(0,1),(0,0)]
On the 3 X 3 torus, the 22 walks are all equivalent to the following eleven walks by switching coordinates:
  [(0,0),(0,1),(0,2),(0,0)]
  [(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(0,0)]
  [(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(0,0)]
  [(0,0),(0,1),(1,1),(1,2),(2,2),(0,2),(0,0)]
  [(0,0),(0,1),(1,1),(1,2),(2,2),(2,0),(0,0)]
  [(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(0,0)]
  [(0,0),(0,1),(0,2),(1,2),(2,2),(2,0),(0,0)]
  [(0,0),(0,1),(0,2),(1,2),(1,0),(2,0),(0,0)]
  [(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(1,2),(1,0),(2,0),(0,0)]
  [(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(2,1),(2,2),(0,2),(0,0)]
  [(0,0),(0,1),(0,2),(1,2),(1,0),(1,1),(2,1),(2,2),(2,0),(0,0)]

Crossrefs

Cf. A000984, A324604.

Sequence in context: A339781 A377358 A192332 * A322520 A349765 A018279

Adjacent sequences: A324600 A324601 A324602 * A324604 A324605 A324606

Keyword

nonn,more,walk

Author

Peter Kagey, Mar 09 2019

Status

approved