A380813 Sequence of y-coordinates of the lexicographically earliest (according to the spiral numbering of the square grid; see comments) infinite Racetrack trajectory (using von Neumann neighborhood) on the square grid.

0, 0, -1, -2, -3, -3, -2, -1, 1, 2, 3, 3, 2, 1, 0, -1, -1, 0, 2, 3, 4, 5, 5, 4, 2, 0, -2, -4, -5, -6, -6, -5, -4, -2, 0, 2, 4, 5, 6, 6, 6, 5, 3, 1, -1, -3, -4, -4, -4, -3, -1, 1, 3, 5, 6, 7, 7, 7, 6, 4, 2, 0, -2, -3, -4, -5, -5, -4, -3, -2, -1, 0, 1, 1, 0, -1

Offset

0,4

Comments

See A380813 for more details.

See A351042 or Wikipedia link for a description of the rules of Racetrack.

The trajectory in A351043 is defined in a similar way, but it does not backtrack when it gets stuck, so it is finite, ending after 146 steps. The trajectory here is identical to the trajectory in A351043 for the first 144 steps, and it turns out that the y-coordinates agree also for the last 2 steps.

Links

Pontus von Brömssen, Table of n, a(n) for n = 0..10000

Pontus von Brömssen, Plot of the first 5000 steps of the trajectory.

Wikipedia, Racetrack.

Formula

a(n) = A274923(A351043(n)+1) for n <= 146.

Crossrefs

Cf. A274923, A351042, A351043, A380812 (x-coordinates), A380814.

Sequence in context: A123548 A131838 A274885 * A287732 A334223 A171414

Adjacent sequences: A380810 A380811 A380812 * A380814 A380815 A380816

Keyword

sign

Author

Pontus von Brömssen, Feb 05 2025

Status

approved