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A229216
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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.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..109.
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
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EXAMPLE
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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.
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CROSSREFS
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Cf. A229217.
Sequence in context: A119910 A130784 A138034 * A087818 A112746 A107460
Adjacent sequences: A229213 A229214 A229215 * A229217 A229218 A229219
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KEYWORD
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easy,sign
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AUTHOR
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Arie Bos, Sep 25 2013
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STATUS
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approved
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