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

Author

Pontus von Brömssen, Feb 01 2022

Keywords

• nonn
• more

Examples

			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.
		

Links

• Wikipedia, Racetrack

Crossrefs

Main diagonal of A351108.

Cf. A007764, A351042, A351107.