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A349008
Area of the convex hull around R5 dragon curve expansion level n.
4
0, 2, 16, 106, 578, 2954, 15064, 75908, 380334, 1904330, 9528618, 47654840, 238295096, 1191556256, 5957936770, 29789860126, 148950201902, 744752899780, 3723767329212, 18618843605284, 93094240114350, 465471240742354, 2327356261817746, 11636781564585616
OFFSET
0,2
COMMENTS
Expansion level n is the first 5^n segments of the curve and so the hull is around X,Y points located at X=A349195(t), Y=A349196(t) for t = 0..5^n.
LINKS
Kevin Ryde, Iterations of the R5 Dragon Curve, see index "HA".
Kevin Ryde, PARI/GP Code
FORMULA
For n>=2, a(n) = 17*5^(n-2) - 1 + Sum_{j=1..n-2} ( (3*5^(n-2-j)-1)*HAgrow(2*b^j) + 2*5^(n-2-j)*HAgrow((4-i)*b^j) ),
where complex b=1+2*i and
HAgrow(z) = MinReIm(ShearRe(RotQ(z))),
MinReIm(z) = min(abs(Re z),abs(Im z)),
ShearRe(z) = z + Re(z),
RotQ(z) = z if sign(Re z) = sign(Im z) or RotQ(z) = z*i otherwise.
EXAMPLE
For n=2 the curve is:
@--@
|
*--* *--* *--@ Hull vertices "@".
| | | | | Hull area a(2) = 16.
*--*--*--*--*--*
| | | | |
@--* *--* *--*
|
@--@
PROG
(PARI) See links.
CROSSREFS
Cf. A349195, A349196 (coordinates).
Cf. A349009 (fractal area).
Sequence in context: A236958 A009619 A012024 * A366635 A193217 A329550
KEYWORD
nonn,easy
AUTHOR
Kevin Ryde, Nov 06 2021
STATUS
approved