A229216 - OEIS

%I #12 Oct 08 2020 19:21:37

%S 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,

%T -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,

%U 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

%N 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.

%C The sequence is generated by:

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

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

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

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

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

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

%H Arie Bos, <a href="http://arxiv.org/abs/1210.7123">Index notation of grid graphs</a>, arXiv:1210.7123 [cs.CG], 2012.

%H Skylyn Irby, Sandra Spiroff, <a href="https://doi.org/10.4134/BKMS.b190723">On conditionally defined Fibonacci and Lucas sequences and periodicity</a>, Bull. Korean Math. Soc. (2020) Vol. 57, No. 4, 1033-1048.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Koch_snowflake">Koch snowflake</a>

%e Start 1,3,-2,

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

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

%e With each step the length increases by a factor 4.

%Y Cf. A229217.

%K easy,sign

%O 1,2

%A _Arie Bos_, Sep 25 2013