A334483 a(n) is the X-coordinate of the n-th point of the Sierpinski arrowhead curve; sequence A334484 gives Y-coordinates.

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

Offset

0,7

Comments

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:

Y

/

/

0 ---- X

The Sierpinski arrowhead curve can be represented using an L-system.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..2187

Rémy Sigrist, Colored line plot of the first 3^7+1 points of the Sierpinski arrowhead curve (where the hue is function of the number of steps from the origin)

Rémy Sigrist, PARI program for A334483

Wikipedia, Arrowhead curve

Index entries for sequences related to coordinates of 2D curves

Formula

A262174(1 + a(n) + A334484(n), 1 + A334484(n)) = 1 + n for any n >= 0.

Example

The Sierpinski arrowhead curve starts (on a hexagonal lattice) as follows:
                         +
                        27\
                           \
                            +
                           /26
                          /
                    +----+
                   /24   25
                  /
                 +          +----+
                23\        /20  19\
                   \      /        \
                    +----+          +
                    22   21        /18
                                  /
            +----+               +
           /4    5\             17\
          /        \               \
         +          +               +----+
         3\        /6               16  15\
           \      /                        \
            +    +          +----+          +
           /2    7\        /10  11\        /14
          /        \      /        \      /
    +----+          +----+          +----+
    0    1          8    9          12   13
- hence a(6) = a(7) = a(20) = a(21) = 2.

Prog

(PARI) See Links section.

Crossrefs

Cf. A262174, A307672, A334484.

Sequence in context: A341904 A237638 A343205 * A261093 A306726 A188511

Adjacent sequences: A334480 A334481 A334482 * A334484 A334485 A334486

Keyword

nonn,look

Author

Rémy Sigrist, May 03 2020

Status

approved