A360170 a(n) is the X-coordinate after n steps of an infinite knight's tour through all lattice points; see A360171 for the Y-coordinates.

0, 1, -1, -2, 0, 2, 1, -1, -2, -1, 1, 2, 0, -2, -1, 1, 2, 0, -2, -1, -2, 0, 2, 1, 2, 3, 1, -1, -3, -4, -3, -4, -2, 0, 2, 4, 3, 4, 3, 1, -1, -3, -4, -3, -4, -3, -1, 1, 3, 4, 3, 4, 2, 0, -2, -4, -3, -4, -3, -1, 1, 3, 4, 3, 4, 2, 0, -2, -4, -3, -4, -3, -4, -2, 0

Offset

0,4

Comments

See A068608 for similar sequences.

Links

Table of n, a(n) for n=0..74.

Robert Bosch and Zejian Huang, Structured Knight’s Tours

Mathematics StackExchange, Infinite Knight's Tour

Rémy Sigrist, Illustration of the first steps (where colors denote the direction to the next position)

Rémy Sigrist, PARI program

Dan Thomasson, Knight's Tour Art

Wikipedia, Knight's tour

Wolfram Demonstrations Project, An Infinite Knight's Tour

Index entries for sequences related to coordinates of 2D curves

Formula

a(n) = A174344(A068613(n+1)).

Example

See illustration of the first steps in Links section.

Prog

(PARI) See Links section.

Crossrefs

Cf. A068608, A068613, A174344, A360171.

Sequence in context: A281460 A035226 A126043 * A306659 A191225 A223893

Adjacent sequences: A360167 A360168 A360169 * A360171 A360172 A360173

Keyword

sign

Author

Rémy Sigrist, Jan 28 2023

Status

approved