A351107 Number of simple paths for a Racetrack car (using Moore neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an n X n grid.

1, 3, 23, 1470, 914525

Offset

1,2

Links

Table of n, a(n) for n=1..5.

Wikipedia, Racetrack

Example

For n = 3 the following paths exist (up to reflection in the diagonal). The numbers give the positions of the car after successive steps.
  ..2  ..3  ..3  ..3  ..4  ..4  .34  .56  456  548  678  678
  .1.  ..2  .2.  .12  ..3  .23  .2.  .43  32.  673  543  512
  0..  01.  01.  0..  012  01.  01.  012  01.  012  012  043
Of these, only the first path is symmetric with respect to the diagonal, so the other 11 give rise to 2 paths each. In total, there are a(3) = 1 + 2*11 = 23 possible paths.

Crossrefs

Main diagonal of A351106.

Cf. A140518, A351041, A351109, A351111.

Sequence in context: A144986 A088056 A009593 * A009818 A210734 A166315

Adjacent sequences: A351104 A351105 A351106 * A351108 A351109 A351110

Keyword

nonn,more

Author

Pontus von Brömssen, Feb 01 2022

Status

approved