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