A351108 -id:A351108 - cp's OEIS frontend

A351106 Triangle read by rows: T(m,n) is the 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 m X n grid, 1 <= n <= m.

1, 1, 3, 1, 6, 23, 2, 17, 118, 1470, 3, 47, 762, 23878, 914525, 5, 133, 5724, 420894, 40285572

Offset: 1

Pontus von Brömssen, Jan 31 2022

			Triangle begins:
  m\n| 1   2    3      4        5  6
  ---+------------------------------
  1  | 1
  2  | 1   3
  3  | 1   6   23
  4  | 2  17  118   1470
  5  | 3  47  762  23878   914525
  6  | 5 133 5724 420894 40285572  ?

Wikipedia, Racetrack

Cf. A291896 (column n=1), A329118, A351041, A351107 (main diagonal), A351108, A351110.

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.

Original entry on oeis.org

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

Offset: 1

Pontus von Brömssen, Feb 01 2022

			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.

Wikipedia, Racetrack

Main diagonal of A351108.

Cf. A007764, A351042, A351107.

cp's OEIS Frontend

A351106 Triangle read by rows: T(m,n) is the 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 m X n grid, 1 <= n <= m.

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