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A349008
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Area of the convex hull around R5 dragon curve expansion level n.
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4
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0, 2, 16, 106, 578, 2954, 15064, 75908, 380334, 1904330, 9528618, 47654840, 238295096, 1191556256, 5957936770, 29789860126, 148950201902, 744752899780, 3723767329212, 18618843605284, 93094240114350, 465471240742354, 2327356261817746, 11636781564585616
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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.
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EXAMPLE
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For n=2 the curve is:
@--@
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*--* *--* *--@ Hull vertices "@".
| | | | | Hull area a(2) = 16.
*--*--*--*--*--*
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@--* *--* *--*
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@--@
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PROG
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(PARI) See links.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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