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Movement sequence in the counter-clockwise undulating spiral, whereby 1, 2, 3, 4 represent moves to the right, down, left and up.
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%I #21 Jan 20 2024 09:12:54

%S 1,4,3,4,3,2,3,2,1,2,1,2,1,4,1,4,1,4,3,4,3,4,3,4,3,2,3,2,3,2,3,2,1,2,

%T 1,2,1,2,1,2,1,4,1,4,1,4,1,4,1,4,3,4,3,4,3,4,3,4,3,4,3,2,3,2,3,2,3,2,

%U 3,2,3,2,1,2,1,2,1,2,1,2,1,2,1,2,1,4,1,4,1,4,1,4,1,4

%N Movement sequence in the counter-clockwise undulating spiral, whereby 1, 2, 3, 4 represent moves to the right, down, left and up.

%C y ^

%C |

%C 4 | 2---3

%C | | |

%C 3 | 2---3 4---3

%C | | |

%C 2 | 2---3 2---3 4---3

%C | | | | |

%C 1 | 2---3 2---3 4---3 4---3

%C | | | | |

%C 0 | 1---2 1---2 1---4 1---4

%C | | | | |

%C -1 | 1---2 1-- 2 1---4 1---4

%C | | | | |

%C -2 | 1---2 1---4 1---4

%C | | |

%C -3 | 1---2 1---4

%C | | |

%C -4 | 1---4

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

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

%F a(k1)=1 with k1=i^2*8+i*0+2*j+1 with i,j >= 0 and j<=4i.

%F a(k2)=2 with k2=i^2*8+i*12+2*j+6 with i,j >= 0 and j<=4*i+3.

%F a(k3)=3 with k3=i^2*8+i*8+2*j+3 with i,j >= 0 and j<=4*i+2.

%F a(k4)=4 with k4=i^2*8+i*4+2*j+2 with i,j >= 0 and j<=4*i+1.

%Y Cf. A359058, A359216, A359217, A063826.

%K nonn,walk

%O 1,2

%A _Hans G. Oberlack_, Dec 04 2023