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A339739
a(n) gives the number of squares in the n-th iteration of the Harter-Heighway dragon.
0
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
1,5
COMMENTS
a(n) >= A003230(n-4) for n >= 4, and a(n) > A003230(n-4) for n >= 7.
LINKS
Code Golf Stack Exchange user Domenico Modica, Eye test - How many squares are in this picture?
Wikipedia, Dragon Curve
EXAMPLE
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.
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*---* *
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*---*
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*---*---* *---* *---*
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*---* *---*---*---* *---*
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*---*---* *---*
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*---*
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.
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CROSSREFS
A003230 gives the number of 1 X 1 squares.
Sequence in context: A102281 A269083 A026583 * A291238 A110034 A340824
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Jan 05 2021
EXTENSIONS
a(17)-a(26) from Bert Dobbelaere, Jun 15 2024
STATUS
approved