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.
Original entry on oeis.org
1, 1, 3, 1, 6, 23, 2, 17, 118, 1470, 3, 47, 762, 23878, 914525, 5, 133, 5724, 420894, 40285572
Offset: 1
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 ?
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
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.
A351111
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 n X n grid, such that all positions are visited exactly once.
Original entry on oeis.org
1, 0, 6, 2, 9436
Offset: 1
For n = 4 the following path and its reflection in the diagonal are the only solutions, so a(4) = 2.
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