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

Author

Max Barrentine, Sep 13 2015

Keywords

• nonn
• tabl
• look

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.

Examples

			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;
   ...
		

Links

• Max Barrentine, Table of n, a(n) for n = 1..2144
• Wikipedia, Sierpiński arrowhead curve

Crossrefs

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