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a(n) is the Y-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332246 gives X-coordinates.
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%I #20 Feb 12 2020 16:13:05

%S 0,0,1,1,0,-1,-1,0,0,1,1,2,2,2,3,3,4,4,5,5,4,3,3,4,4,3,3,2,2,2,1,1,0,

%T -1,-1,-2,-2,-2,-3,-3,-4,-4,-3,-3,-4,-5,-5,-4,-4,-3,-3,-2,-2,-2,-1,-1,

%U 0,0,1,1,0,-1,-1,0,0,1,1,2,2,2,3,3,4,4,3,3,4,5

%N a(n) is the Y-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332246 gives X-coordinates.

%C This sequence is the imaginary part of {f(n)} defined as:

%C - f(0) = 0,

%C - f(n+1) = f(n) + i^t(n)

%C where t(n) is the number of 1's and 6's minus the number of 3's and 4's

%C in the base 8 representation of n

%C and i denotes the imaginary unit.

%H Rémy Sigrist, <a href="/A332247/b332247.txt">Table of n, a(n) for n = 0..4096</a>

%H Robert Ferréol (MathCurve), <a href="https://www.mathcurve.com/fractals/minkowski/minkowski.shtml">Saucisse de Minkowski</a> [in French]

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Minkowski_Sausage">Minkowski sausage</a>

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

%F a(8^k-m) = -a(m) for any k >= 0 and m = 0..8^k.

%o (PARI) { dd = [0,1,0,-1,-1,0,1,0]; z=0; for (n=0, 77, print1 (imag(z)", "); z += I^vecsum(apply(d -> dd[1+d], digits(n, #dd)))) }

%Y Cf. A332246 (X-coordinates and additional comments).

%K sign,look,base

%O 0,12

%A _Rémy Sigrist_, Feb 08 2020