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A229217 If 1 and 2 represent the 2D vectors (1,0) and (0,1) and -1 and -2 are the negation of these vectors, then this sequence represents the Koch curve. 1
1, 2, 1, -2, 1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, 2, -1, 2, 1, 2, -1, -2, -1, 2, -1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, -1, -2, -1, 2, -1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, 2, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is generated by the rewriting rules:

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

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

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

P(-2) = -2,1,-2,-1,-2, so P(-x)=-P(x).

The start is 1.

LINKS

Table of n, a(n) for n=1..107.

Arie Bos, Index notation of grid graphs

Wikipedia, Koch curve

EXAMPLE

Start with 1, you get

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

in the 2nd step 1,2,1,-2,1,2,-1,2,1,2,1,2,1,-2,1,-2,1,-2,-1,-2,1,2,1,-2,1.

With each step the length increases by a factor 5.

CROSSREFS

Cf. A229216, A166253.

Sequence in context: A000034 A040001 A134451 * A167965 A270370 A167966

Adjacent sequences:  A229214 A229215 A229216 * A229218 A229219 A229220

KEYWORD

sign

AUTHOR

Arie Bos, Sep 25 2013

STATUS

approved

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Last modified February 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)