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a(n) is the Y-coordinate of the n-th point of the Fibonacci word fractal. Sequence A332298 gives X-coordinates.
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%I #19 Aug 20 2020 21:19:37

%S 0,0,0,-1,-1,-1,0,1,1,2,3,3,4,5,5,5,4,4,4,5,6,6,7,8,8,9,10,10,10,9,9,

%T 9,10,10,10,9,8,8,7,6,6,6,7,7,7,6,6,6,7,8,8,9,10,10,10,9,9,9,10,10,10,

%U 9,8,8,7,6,6,5,4,4,4,5,5,5,4,3,3,2,1,1,0,-1

%N a(n) is the Y-coordinate of the n-th point of the Fibonacci word fractal. Sequence A332298 gives X-coordinates.

%H Rémy Sigrist, <a href="/A332299/b332299.txt">Table of n, a(n) for n = 0..10946</a>

%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%o (PARI) A003849(n)=my(k=2); while(fibonacci(k)<=n, k++); while(n>1, while(fibonacci(k--)>n, ); n-=fibonacci(k)); n==1

%o { z=0; d=I; for (n=0, 81, print1 (imag(z) ", "); if (A003849(n)==0, if (n%2==0, d/=I, d*=I);); z+=d) }

%Y Cf. A003849, A265318, A332298 (X-coordinates and additional comments).

%K sign,look

%O 0,10

%A _Rémy Sigrist_, Feb 09 2020