A359058 a(n) = squared distance to the origin of the n-th vertex on a counterclockwise undulating spiral in a square grid.

0, 1, 2, 1, 4, 5, 2, 5, 4, 1, 2, 1, 4, 5, 2, 5, 4, 9, 10, 5, 8, 5, 10, 9, 16, 17, 10, 13, 8, 13, 10, 17, 16, 9, 10, 5, 8, 5, 10, 9, 16, 17, 10, 13, 8, 13, 10, 17, 16, 25, 26, 17, 20, 13, 18, 13, 20, 17, 26, 25, 36, 37, 26, 29, 20, 25, 18, 25, 20, 29, 26, 37, 36, 25, 26, 17, 20, 13, 18, 13, 20

Offset: 0

Author

Hans G. Oberlack, Dec 14 2022

Keywords

• nonn
• easy

Comments

The spiral coordinates are A359216 and A359217.

Examples

			The spiral begins as follows and for instance point n=7 is at x=-2,y=1 so that a(7) = (-2)^2 + 1^2 = 5.
   y ^
     |
   4 |             17--16
     |              |   |
   3 |         13--10   9--10
     |          |           |
   2 |     13---8   5---4   5---8
     |      |       |   |       |
   1 | 17--10   5---2   1---2   5--10
     |  |       |           |       |
   0 | 16---9   4---1   0---1   4---9
     |      |       |           |       |
  -1 |     10---5   2---1   2---5  10--17
     |          |       |   |       |
  -2 |          8---5   4---5   8--13
     |              |           |
  -3 |             10---9  10--13
     |                  |   |
  -4 |                 16--17
     +------------------------------------>
       -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, Undulating counterclockwise spiral in a square grid
• Rémy Sigrist, PARI program

Crossrefs

Cf. A001481, A336336, A359216, A359217.

Programs

PARI

See Links section.

Formula

a(n) = A359216(n)^2 + A359217(n)^2.