A324607 The y-coordinates of squares visited by knight moves on a spirally numbered board and moving to the lowest available unvisited square at each step.

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

Offset: 1

Author

Peter Kagey, Jun 06 2019

Keywords

• sign
• fini
• full
• walk

Links

• Peter Kagey, Table of n, a(n) for n = 1..2016
• N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019)
• Visualization of walk using Plot 2. - _Peter Kagey_, Jul 15 2019

Crossrefs

Cf. A274923, A316667.

A324606 gives x-coordinates.

Formula

a(n) = A274923(A316667(n)).