A262174 Sierpiński arrowhead curve as a triangular array starting leftward from the top, read by rows.

1, 2, 0, 0, 3, 4, 9, 8, 0, 5, 10, 0, 7, 6, 0, 0, 11, 0, 0, 23, 24, 13, 12, 0, 0, 22, 0, 25, 14, 0, 17, 18, 0, 21, 26, 0, 0, 15, 16, 0, 19, 20, 0, 27, 28, 69, 68, 0, 0, 0, 0, 0, 0, 0, 29, 70, 0, 67, 0, 0, 0, 0, 0, 31, 30, 0, 0, 71, 66, 0, 0, 0, 0, 0, 32, 0, 35, 36

Offset

1,2

Comments

The triangle up to the (1 + 2^n)th row is the n-th iteration of the curve, rotated such that the curve begins at the top and continues down to the left.

As this is not a space-filling curve, not all points on the triangular lattice are reached by the curve; these points are given the value 0.

Links

Max Barrentine, Table of n, a(n) for n = 1..2144

Wikipedia, Sierpiński arrowhead curve

Example

The first 5 rows of this triangle show how this curve begins (connect the terms in numerical order):
            1;
          2,  0;
        0,  3,  4;
      9,  8,  0,  5;
   10,  0,  7,  6,  0;
   ...

Crossrefs

See also A163357, A163334, and A054238 for other fractal curves.

Sequence in context: A230414 A053653 A332629 * A064146 A361100 A336309

Adjacent sequences: A262171 A262172 A262173 * A262175 A262176 A262177

Keyword

nonn,tabl,look

Author

Max Barrentine, Sep 13 2015

Status

approved