A349320 a(n) is the Y-coordinate of the n-th point of the hexdragon curve; sequence A349319 gives X-coordinates.

0, 0, 1, 2, 3, 3, 4, 5, 5, 4, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 11, 10, 10, 11, 11, 10, 9, 9, 8, 7, 7, 8, 8, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 14, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 20, 19, 19, 20, 20, 19, 18, 18, 17, 16, 16, 17, 17, 16, 16, 17, 17

Offset

0,4

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 hexdragon curve can be represented using an L-system obtained from that of the terdragon curve by replacing each "move forward and turn +-120 degrees" step by two "move forward and turn +- 60 degrees" steps.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..4373

Joerg Arndt, Matters Computational (The Fxtbook), section 1.31.4 Terdragon and hexdragon.

Rémy Sigrist, Representation of the hexdragon curve after 6 iterations

Rémy Sigrist, PARI program for A349320

Index entries for sequences related to coordinates of 2D curves

Example

The hexdragon curve starts as follows:
              16-17
              /
            15
              \
              14
              /
         12-13
         /
       11      8--7
         \    /    \
         10--9      6
                   /
               4--5
              /
             3
              \
               2
              /
          0--1
- so a(0) = a(1) = 0,
     a(2) = 1,
     a(3) = 2,
     a(4) = a(5) = 3,
     a(6) = a(9) = a(10) = 4,
     a(7) = a(8) = a(11) = 5,
     a(12) = a(13) = 6,
     a(14) = 7,
     a(15) = 8,
     a(16) = a(17) = 9.

Prog

(PARI) See Links section.

Crossrefs

See A349041 for a similar sequence.

Cf. A349319.

Sequence in context: A361383 A240153 A241435 * A078338 A338587 A338580

Adjacent sequences: A349317 A349318 A349319 * A349321 A349322 A349323

Keyword

sign

Author

Rémy Sigrist, Nov 14 2021

Status

approved