# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a332384
Showing 1-1 of 1

%I A332384 #18 Apr 15 2022 13:02:22
%S A332384 0,0,1,1,2,2,1,1,2,2,1,1,0,0,-1,-1,0,0,-1,-1,-2,-2,-1,-1,-2,-2,-3,-3,
%T A332384 -4,-4,-5,-5,-4,-4,-5,-5,-6,-6,-5,-5,-6,-6,-5,-5,-4,-4,-3,-3,-4,-4,-5,
%U A332384 -5,-6,-6,-5,-5,-6,-6,-7,-7,-8,-8,-9,-9,-8,-8,-9,-9,-10
%N A332384 a(n) is the Y-coordinate of the n-th point of the dragon curve. Sequence A332383 gives X-coordinates.
%H A332384 Rémy Sigrist, <a href="/A332384/b332384.txt">Table of n, a(n) for n = 0..8192</a>
%H A332384 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A332384 For any k >= 0:
%F A332384 - a(2^(4*k))   =        0,
%F A332384 - a(2^(4*k+1)) =   (-4)^k,
%F A332384 - a(2^(4*k+2)) = 2*(-4)^k,
%F A332384 - a(2^(4*k+3)) = 2*(-4)^k.
%t A332384 Im[Join[{0}, Accumulate[Nest[Join[#, Reverse[I #]] &, {1}, 7]]]] (* _Vladimir Reshetnikov_, Apr 14 2022 *)
%o A332384 (PARI) A014577(n)=1/2*(1+(-1)^(1/2*((n+1)/2^valuation(n+1, 2)-1)))
%o A332384 { z=0; d=1; for (n=0, 68, print1 (imag(z) ", "); z += d; d*=if (A014577(n), +I, -I)) }
%Y A332384 Cf. A014577, A332383 (X-coordinates and additional comments).
%K A332384 sign,base
%O A332384 0,5
%A A332384 _Rémy Sigrist_, Feb 10 2020

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE