A349198 a(n) is the Y-coordinate of the n-th point of the alternate terdragon curve; sequence A349197 gives X-coordinates.

0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, -1, -1, -2, -1, -2, -1, -2, -2, -3, -3, -2, -2, -3, -3, -4, -4, -3, -3, -2, -3, -2, -2, -1, -1, 0, -1, 0, 0, 1, 1, 0

Offset

0,15

Comments

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows (the Y-axis corresponds to the sixth primitive root of unity):

Y

/

/

0 ---- X

The alternate terdragon curve can be represented using an L-system.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6561

Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves -- I and II, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. Reprinted in Donald E. Knuth, Selected Papers on Fun and Games, 2011, pages 571-614.

Rémy Sigrist, Colored representation of the first 1 + 9^6 points of the alternate terdragon curve (where the hue is function of the number of steps from the origin)

Rémy Sigrist, PARI program for A349198

Index entries for sequences related to coordinates of 2D curves

Formula

a(9^k) = 0 for any k >= 0.

a(9*n) = 3*a(n).

Example

The alternate terdragon curve starts as follows:
                  14
                   \
                    \
         2----3,12--10,13
          \   / \   / \
           \ /   \ /   \
      0----1,4--5,8,11--9
                 / \
                /   \
               6-----7
- so a(0) = a(1) = a(4) = a(5) = a(8) = a(9) = a(11) = 0,
     a(6) = a(7) = -1,
     a(2) = a(3) = a(10) = a(12) = a(13) = 1.

Prog

(PARI) See Links section.

Crossrefs

See A349041 for a similar sequence.

Cf. A349197.

Sequence in context: A092333 A303297 A107452 * A205018 A286716 A029213

Adjacent sequences: A349195 A349196 A349197 * A349199 A349200 A349201

Keyword

sign

Author

Rémy Sigrist, Nov 10 2021

Status

approved