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

0, 1, 1, 0, 0, 1, 1, 0, -1, -1, -2, -3, -3, -2, -2, -3, -3, -2, -2, -3, -4, -4, -5, -6, -7, -7, -6, -5, -4, -4, -5, -6, -7, -7, -8, -9, -9, -8, -8, -9, -9, -8, -8, -9, -10, -10, -11, -12, -12, -11, -11, -12, -12, -11, -11, -12, -13, -13, -14, -15, -16, -16

Offset

0,11

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 A349319

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(3) = a(4) = a(7) = 0,
     a(1) = a(2) = a(5) = a(6) = 1,
     a(8) = a(9) = -1,
     a(10) = a(13) = a(14) = a(17) = -2,
     a(11) = a(12) = a(15) = a(16) = -3.

Prog

(PARI) See Links section.

Crossrefs

See A349040 for a similar sequence.

Cf. A349320.

Sequence in context: A269043 A309952 A059252 * A251619 A030620 A348241

Adjacent sequences: A349316 A349317 A349318 * A349320 A349321 A349322

Keyword

sign

Author

Rémy Sigrist, Nov 14 2021

Status

approved