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.

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

1,6

Links

Table of n, a(n) for n=1..36.

Wikipedia, Racetrack

Example

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

Crossrefs

Cf. A064297, A291896 (column n=1), A351042, A351106, A351109 (main diagonal).

Sequence in context: A134890 A101360 A270371 * A184311 A110910 A119532

Adjacent sequences: A351105 A351106 A351107 * A351109 A351110 A351111

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Feb 01 2022

Status

approved