OFFSET
0,2
COMMENTS
LINKS
Kevin Ryde, Table of n, a(n) for n = 0..400
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
KEYWORD
nonn,easy
AUTHOR
Kevin Ryde, Nov 06 2021
STATUS
approved