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

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%I A339739 #39 Jun 15 2024 15:25:42
%S A339739 0,0,0,1,4,11,30,78,205,546,1455,4062,11192,31889,88487,254594,710683,
%T A339739 2047705,5711439,16455169,45894868,132118562,368149344,1059171430,
%U A339739 2950384277,8484556353
%N A339739 a(n) gives the number of squares in the n-th iteration of the Harter-Heighway dragon.
%C A339739 a(n) >= A003230(n-4) for n >= 4, and a(n) > A003230(n-4) for n >= 7.
%H A339739 Code Golf Stack Exchange user Domenico Modica, <a href="https://codegolf.stackexchange.com/q/216919/53884">Eye test - How many squares are in this picture?</a>
%H A339739 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dragon_curve#Heighway_dragon">Dragon Curve</a>
%e A339739 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.
%e A339739     *---*
%e A339739     |   |
%e A339739 *---*   *
%e A339739 |
%e A339739 *---*
%e A339739     |
%e A339739 *---*---*   *---*   *---*
%e A339739 |   |   |   |   |   |   |
%e A339739 *---*   *---*---*---*   *---*
%e A339739             |   |           |
%e A339739         *---*---*       *---*
%e A339739         |   |
%e A339739         *---*
%e A339739 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.
%e A339739        _   _
%e A339739       |_|_| |_
%e A339739    _   _|    _|
%e A339739   |_|_|_
%e A339739     |_|_|
%e A339739       |_   _       _       _
%e A339739    _   _|_|_|    _|_|    _|_|
%e A339739   |_|_|_|_|_   _|_|_   _|_|_   _
%e A339739     |_| |_| |_|_|_|_|_| |_| |_|_|
%e A339739               |_|_|_|_        |_
%e A339739            _   _|_| |_|        _|
%e A339739           |_|_|_|_          |_|
%e A339739             |_| |_|
%Y A339739 A003230 gives the number of 1 X 1 squares.
%K A339739 nonn,more
%O A339739 1,5
%A A339739 _Peter Kagey_, Jan 05 2021
%E A339739 a(17)-a(26) from _Bert Dobbelaere_, Jun 15 2024