A339739 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

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

LINKS

Table of n, a(n) for n=1..26.

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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*---* *---*---*---* *---*

| | |

*---*---* *---*

| |

*---*

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

Adjacent sequences: A339736 A339737 A339738 * A339740 A339741 A339742

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Jan 05 2021

EXTENSIONS

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

STATUS

approved