A349196 a(n) is the Y-coordinate of the n-th point of the R5 dragon curve; A349195 gives X-coordinates.

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

Offset: 0

Author

Rémy Sigrist, Nov 10 2021

Keywords

• sign

Comments

The R5 dragon curve can be represented using an L-system.

Examples

			The R5 dragon curve starts as follows:
         +-----+
       24|   25
         |
         |
         +-----+     +-----+     +-----+
       23    22|   11|   10|    7|    6|
               |     |     |     |     |
             21|   12|    9|    8|     |
         +-----+-----+-----+-----+-----+
       20|   17|   16|   13|    4|    5
         |     |     |     |     |
         |     |     |     |     |
         +-----+     +-----+     +-----+
       19    18    15    14     3     2|
                                       |
                                       |
                                 +-----+
                                0     1
- so a(0) = a(1) = 0,
     a(2) = a(3) = a(14) = a(15) = a(18) = a(19) = 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..3125
• Kevin Ryde, Iterations of the R5 Dragon Curve
• Rémy Sigrist, Colored representation of the first 1 + 5^9 points of the R5 dragon curve (where the hue is function of the number of steps from the origin)
• Rémy Sigrist, PARI program for A349196
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A006496, A349008, A349009, A349010, A349195.

Programs

PARI

See Links section.

Formula

a(5^k) = A006496(k) for any k >= 0.