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A229216 If 1, 2, and 3 represent the three 2D vectors (1,0), (0.5,sqrt(3)) and (-0.5,sqrt(3)) and -1, -2 and -3 are the negation of these vectors, then this sequence represents Koch's snowflake. 1
1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, 1, -3, 2, 1, -3, -2, 1, -3, -2, -1, -3, -2, 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, 1, -3, 2, 1, 3, 2, -1, 3, 2, 1, 3, 2, 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, 1, -3, 2, 1, 3, 2, -1, 3, 2, 1, 3, 2, -1, 3, -2, -1, 3, 2, -1, 3, 2, 1, 3, 2, 1, -3, 2, 1, 3, 2, -1, 3, 2, 1, 3, 2, -1, 3, -2, -1, 3, 2, -1, 3, -2, -1, -3, -2, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is generated by:

P(1) = 1,-3,2,1,

P(2) = 2,1,3,2,

P(3) = 3,2,-1,3,

P(-1) = -1,3,-2,-1,

P(-2) = -2,-1,-3,-2,

P(-3) = -3,-2,1,-3 (we have P(-x)=-P(x)), and 1, 3, -2 is the start.

LINKS

Table of n, a(n) for n=1..109.

Arie Bos, Index notation of grid graphs

Wikipedia, Koch snowflake

EXAMPLE

Start 1,3,-2,

in the first step 1,-3,2,1,3,2,-1,3,-2,-1,-3,-2 and

in the second step 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, ..., -2, -1, -3, -2.

With each step the length increases by a factor 4.

CROSSREFS

Cf. A229217.

Sequence in context: A119910 A130784 A138034 * A087818 A112746 A107460

Adjacent sequences:  A229213 A229214 A229215 * A229217 A229218 A229219

KEYWORD

easy,sign

AUTHOR

Arie Bos, Sep 25 2013

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)