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

0,3

Comments

The spiral coordinates are A359216 and A359217.

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

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A001481, A336336, A359216, A359217.

Sequence in context: A053985 A091564 A321301 * A191379 A038574 A212713

Adjacent sequences: A359055 A359056 A359057 * A359059 A359060 A359061

Keyword

nonn,easy

Author

Hans G. Oberlack, Dec 14 2022

Status

approved