A332384 a(n) is the Y-coordinate of the n-th point of the dragon curve. Sequence A332383 gives X-coordinates.

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, -4, -4, -5, -5, -4, -4, -5, -5, -6, -6, -5, -5, -6, -6, -5, -5, -4, -4, -3, -3, -4, -4, -5, -5, -6, -6, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -8, -8, -9, -9, -10

Offset: 0

Author

Rémy Sigrist, Feb 10 2020

Keywords

• sign
• base

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A014577, A332383 (X-coordinates and additional comments).

Programs

Mathematica

Im[Join[{0}, Accumulate[Nest[Join[#, Reverse[I #]] &, {1}, 7]]]] (* Vladimir Reshetnikov, Apr 14 2022 *)

PARI

A014577(n)=1/2*(1+(-1)^(1/2*((n+1)/2^valuation(n+1, 2)-1)))
{ z=0; d=1; for (n=0, 68, print1 (imag(z) ", "); z += d; d*=if (A014577(n), +I, -I)) }

Formula

For any k >= 0:

- a(2^(4*k)) = 0,

- a(2^(4*k+1)) = (-4)^k,

- a(2^(4*k+2)) = 2*(-4)^k,

- a(2^(4*k+3)) = 2*(-4)^k.