A332299 a(n) is the Y-coordinate of the n-th point of the Fibonacci word fractal. Sequence A332298 gives X-coordinates.

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

Offset: 0

Author

Rémy Sigrist, Feb 09 2020

Keywords

• sign
• look

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10946
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

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

Programs

PARI

A003849(n)=my(k=2); while(fibonacci(k)<=n, k++); while(n>1, while(fibonacci(k--)>n, ); n-=fibonacci(k)); n==1
{ 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) }