A351107
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 n X n grid.
Original entry on oeis.org
1, 3, 23, 1470, 914525
Offset: 1
For n = 3 the following paths exist (up to reflection in the diagonal). The numbers give the positions of the car after successive steps.
..2 ..3 ..3 ..3 ..4 ..4 .34 .56 456 548 678 678
.1. ..2 .2. .12 ..3 .23 .2. .43 32. 673 543 512
0.. 01. 01. 0.. 012 01. 01. 012 01. 012 012 043
Of these, only the first path is symmetric with respect to the diagonal, so the other 11 give rise to 2 paths each. In total, there are a(3) = 1 + 2*11 = 23 possible paths.
A351108
Triangle read by rows: T(m,n) is the 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 m X n grid, 1 <= n <= m.
Original entry on oeis.org
1, 1, 0, 1, 1, 2, 2, 2, 3, 8, 3, 3, 7, 12, 40, 5, 7, 13, 26, 160, 1380, 9, 13, 28, 61, 918, 12940, 211164, 14, 27, 61, 161, 7260, 142453, 4997155, 205331148
Offset: 1
Triangle begins:
m\n| 1 2 3 4 5 6 7 8
---+-------------------------------------------
1 | 1
2 | 1 0
3 | 1 1 2
4 | 2 2 3 8
5 | 3 3 7 12 40
6 | 5 7 13 26 160 1380
7 | 9 13 28 61 918 12940 211164
8 | 14 27 61 161 7260 142453 4997155 205331148
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.
Original entry on oeis.org
1, 1, 0, 1, 1, 6, 1, 0, 15, 2, 1, 1, 70, 289, 9436, 1, 0, 294, 191, 128020
Offset: 1
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 ?
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