A351110 Triangle read by rows: T(m,n) is the number of paths for a Racetrack car (using Moore neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an m X n grid, such that all positions are visited exactly once, 1 <= n <= m.

1, 1, 0, 1, 1, 6, 1, 0, 15, 2, 1, 1, 70, 289, 9436, 1, 0, 294, 191, 128020

Offset

1,6

Comments

For a Racetrack car using von Neumann neighborhood (see A351042), there are no such paths if 2 <= n <= m, because the car will never be able to leave a corner of the grid (except the corner where it starts).

Links

Table of n, a(n) for n=1..20.

Wikipedia, Racetrack

Example

Triangle begins:
  m\n| 1  2   3   4      5  6
  ---+-----------------------
  1  | 1
  2  | 1  0
  3  | 1  1   6
  4  | 1  0  15   2
  5  | 1  1  70 289   9436
  6  | 1  0 294 191 128020  ?

Crossrefs

Cf. A000012 (column n=1), A000035 (column n=2), A272445, A351041, A351042, A351106, A351111 (main diagonal).

Sequence in context: A176402 A204013 A127573 * A137388 A302971 A114153

Adjacent sequences: A351107 A351108 A351109 * A351111 A351112 A351113

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Feb 01 2022

Status

approved