A359216 X-coordinates of a point moving in a counterclockwise undulating spiral in a square grid.

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

Offset: 0

Author

Hans G. Oberlack, Dec 21 2022

Keywords

• sign
• walk

Comments

Y-coordinates are given in A359217.

The undulating spiral is

y ^

|

4 | 25--24

| | |

3 | 27--26 23--22

| | |

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

| | | | |

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

| | | | |

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

| | | | |

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

| | | | |

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

| | |

-3 | 38--39 42--43

| | |

-4 | 40--41

+------------------------------------>

-4 -3 -2 -1 0 1 2 3 4 x

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10081
• Hans G. Oberlack, Counterclockwise undulating spiral in a square grid
• Rémy Sigrist, PARI program
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A329116, A359058, A359217.

Programs

PARI

See Links section.

Formula

a(2*n) = A329116(n). - Rémy Sigrist, Apr 01 2023