A351109 Number of simple paths for a Racetrack car (using von Neumann neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an n X n grid.

1, 0, 2, 8, 40, 1380, 211164, 205331148

Offset

1,3

Links

Table of n, a(n) for n=1..8.

Wikipedia, Racetrack

Example

For n = 4 the following paths, together with their reflections in the diagonal, exist. The numbers give the positions of the car after successive steps. In total, there are a(4) = 2*4 = 8 possible paths.
  ...3  ...4  ...4  ...5
  ....  ...3  ..3.  ...4
  ..2.  ..2.  ..2.  ...3
  01..  01..  01..  012.

Crossrefs

Main diagonal of A351108.

Cf. A007764, A351042, A351107.

Sequence in context: A374655 A280921 A208962 * A012597 A012534 A092354

Adjacent sequences: A351106 A351107 A351108 * A351110 A351111 A351112

Keyword

nonn,more

Author

Pontus von Brömssen, Feb 01 2022

Status

approved