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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 Arie Bos, Index notation of grid graphs, arXiv:1210.7123 [cs.CG], 2012. Skylyn Irby, Sandra Spiroff, On conditionally defined Fibonacci and Lucas sequences and periodicity, Bull. Korean Math. Soc. (2020) Vol. 57, No. 4, 1033-1048. 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 April 20 18:45 EDT 2021. Contains 343137 sequences. (Running on oeis4.)