cp's OEIS Frontend

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.

%I A229216 #12 Oct 08 2020 19:21:37
%S A229216 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 A229216 -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 A229216 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 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.
%C A229216 The sequence is generated by:
%C A229216 P(1) = 1,-3,2,1,
%C A229216 P(2) = 2,1,3,2,
%C A229216 P(3) = 3,2,-1,3,
%C A229216 P(-1) = -1,3,-2,-1,
%C A229216 P(-2) = -2,-1,-3,-2,
%C A229216 P(-3) = -3,-2,1,-3 (we have P(-x)=-P(x)), and 1, 3, -2 is the start.
%H A229216 Arie Bos, <a href="http://arxiv.org/abs/1210.7123">Index notation of grid graphs</a>, arXiv:1210.7123 [cs.CG], 2012.
%H A229216 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 A229216 Wikipedia, <a href="http://en.wikipedia.org/wiki/Koch_snowflake">Koch snowflake</a>
%e A229216 Start 1,3,-2,
%e A229216 in the first step 1,-3,2,1,3,2,-1,3,-2,-1,-3,-2 and
%e A229216 in the second step 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, ..., -2, -1, -3, -2.
%e A229216 With each step the length increases by a factor 4.
%Y A229216 Cf. A229217.
%K A229216 easy,sign
%O A229216 1,2
%A A229216 _Arie Bos_, Sep 25 2013