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

%I A360171 #8 Jan 28 2023 12:12:23
%S A360171 0,-2,-1,1,2,1,-1,-2,0,2,1,-1,-2,-1,1,2,0,-1,-2,0,2,1,2,0,-2,-4,-3,-4,
%T A360171 -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,
%U A360171 -3,-1,1,3,4,3,4,2,0,-2,-3,-4,-3,-4,-2,0,2,4,3,4,3
%N A360171 a(n) is the Y-coordinate after n steps of an infinite knight's tour through all lattice points; see A360170 for the X-coordinates.
%C A360171 See A068608 for similar sequences.
%H A360171 Robert Bosch and Zejian Huang, <a href="https://archive.bridgesmathart.org/2021/bridges2021-15.pdf">Structured Knight’s Tours</a>
%H A360171 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/2837079/infinite-knights-tour">Infinite Knight's Tour</a>
%H A360171 Rémy Sigrist, <a href="/A360170/a360170.png">Illustration of the first steps</a> (where colors denote the direction to the next position)
%H A360171 Rémy Sigrist, <a href="/A360171/a360171.gp.txt">PARI program</a>
%H A360171 Dan Thomasson, <a href="http://web.archive.org/web/20070116135830/http://www.borderschess.org/KTart.htm">Knight's Tour Art</a>
%H A360171 Wikipedia, <a href="https://en.wikipedia.org/wiki/Knight%27s_tour">Knight's tour</a>
%H A360171 Wolfram Demonstrations Project, <a href="https://demonstrations.wolfram.com/AnInfiniteKnightsTour/">An Infinite Knight's Tour</a>
%H A360171 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A360171 a(n) = A274923(A068613(n+1)).
%e A360171 See illustration of the first steps in Links section.
%o A360171 (PARI) See Links section.
%Y A360171 Cf. A068608, A068613, A274923, A360170.
%K A360171 sign
%O A360171 0,2
%A A360171 _Rémy Sigrist_, Jan 28 2023