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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.

%I A360170 #10 Jan 28 2023 12:12:15
%S A360170 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,
%T A360170 -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,
%U A360170 -4,-3,-4,-3,-1,1,3,4,3,4,2,0,-2,-4,-3,-4,-3,-4,-2,0
%N 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.
%C A360170 See A068608 for similar sequences.
%H A360170 Robert Bosch and Zejian Huang, <a href="https://archive.bridgesmathart.org/2021/bridges2021-15.pdf">Structured Knight’s Tours</a>
%H A360170 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/2837079/infinite-knights-tour">Infinite Knight's Tour</a>
%H A360170 Rémy Sigrist, <a href="/A360170/a360170.png">Illustration of the first steps</a> (where colors denote the direction to the next position)
%H A360170 Rémy Sigrist, <a href="/A360170/a360170.gp.txt">PARI program</a>
%H A360170 Dan Thomasson, <a href="http://web.archive.org/web/20070116135830/http://www.borderschess.org/KTart.htm">Knight's Tour Art</a>
%H A360170 Wikipedia, <a href="https://en.wikipedia.org/wiki/Knight%27s_tour">Knight's tour</a>
%H A360170 Wolfram Demonstrations Project, <a href="https://demonstrations.wolfram.com/AnInfiniteKnightsTour/">An Infinite Knight's Tour</a>
%H A360170 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A360170 a(n) = A174344(A068613(n+1)).
%e A360170 See illustration of the first steps in Links section.
%o A360170 (PARI) See Links section.
%Y A360170 Cf. A068608, A068613, A174344, A360171.
%K A360170 sign
%O A360170 0,4
%A A360170 _Rémy Sigrist_, Jan 28 2023