A339739 a(n) gives the number of squares in the n-th iteration of the Harter-Heighway dragon.

0, 0, 0, 1, 4, 11, 30, 78, 205, 546, 1455, 4062, 11192, 31889, 88487, 254594, 710683, 2047705, 5711439, 16455169, 45894868, 132118562, 368149344, 1059171430, 2950384277, 8484556353

Offset: 1

Author

Peter Kagey, Jan 05 2021

Keywords

• nonn
• more

Comments

a(n) >= A003230(n-4) for n >= 4, and a(n) > A003230(n-4) for n >= 7.

Examples

			For n = 5, the fifth iteration of the Harter-Heighway dragon has a(5) = 4 squares, as illustrated below. All of the squares are 1 X 1.
    *---*
    |   |
*---*   *
|
*---*
    |
*---*---*   *---*   *---*
|   |   |   |   |   |   |
*---*   *---*---*---*   *---*
            |   |           |
        *---*---*       *---*
        |   |
        *---*
For n = 7, the seventh iteration of the Harter-Heighway dragon has a(7) = 30 squares, as illustrated below. It contains A003230(7) = 28 1 X 1 squares and two 2 X 2 squares.
       _   _
      |_|_| |_
   _   _|    _|
  |_|_|_
    |_|_|
      |_   _       _       _
   _   _|_|_|    _|_|    _|_|
  |_|_|_|_|_   _|_|_   _|_|_   _
    |_| |_| |_|_|_|_|_| |_| |_|_|
              |_|_|_|_        |_
           _   _|_| |_|        _|
          |_|_|_|_          |_|
            |_| |_|
		

Links

• Code Golf Stack Exchange user Domenico Modica, Eye test - How many squares are in this picture?
• Wikipedia, Dragon Curve

Crossrefs

A003230 gives the number of 1 X 1 squares.

Extensions

a(17)-a(26) from Bert Dobbelaere, Jun 15 2024