A351108 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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 * A378298 A184311 A110910

Adjacent sequences: A351105 A351106 A351107 * A351109 A351110 A351111

KEYWORD

nonn,tabl,more

AUTHOR

Pontus von Brömssen, Feb 01 2022

STATUS

approved