%I #36 Apr 01 2023 11:22:41

%S 0,1,1,0,0,-1,-1,-2,-2,-1,-1,0,0,1,1,2,2,3,3,2,2,1,1,0,0,-1,-1,-2,-2,

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

%U 1,0,0,-1,-1,-2,-2,-3,-3,-4,-4,-5,-5,-6,-6,-5,-5,-4

%N X-coordinates of a point moving in a counterclockwise undulating spiral in a square grid.

%C Y-coordinates are given in A359217.

%C The undulating spiral is

%C y ^

%C |

%C 4 | 25--24

%C | | |

%C 3 | 27--26 23--22

%C | | |

%C 2 | 29--28 5---4 21--20

%C | | | | |

%C 1 | 31--30 7---6 3---2 19--18

%C | | | | |

%C 0 | 32--33 8---9 0---1 16--17

%C | | | | |

%C -1 | 34--35 10--11 14--15 46--47

%C | | | | |

%C -2 | 36--37 12--13 44--45

%C | | |

%C -3 | 38--39 42--43

%C | | |

%C -4 | 40--41

%C +------------------------------------>

%C -4 -3 -2 -1 0 1 2 3 4 x

%H Rémy Sigrist, <a href="/A359216/b359216.txt">Table of n, a(n) for n = 0..10081</a>

%H Hans G. Oberlack, <a href="/A359217/a359217.pdf">Counterclockwise undulating spiral in a square grid</a>

%H Rémy Sigrist, <a href="/A359216/a359216.gp.txt">PARI program</a>

%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%F a(2*n) = A329116(n). - _Rémy Sigrist_, Apr 01 2023

%o (PARI) See Links section.

%Y Cf. A329116, A359058, A359217.

%K sign,walk

%O 0,8

%A _Hans G. Oberlack_, Dec 21 2022