A368122 a(n) is the x-coordinate of the n-th point in a square spiral mapped to a square grid rotated by Pi/4 using the symmetrized variant of the distance-limited strip bijection described in A368121.

0, 1, 0, -1, -1, -1, 0, 1, 1, 2, 2, 1, 0, 0, -1, -2, -3, -2, -2, -1, 0, 0, 1, 2, 3, 3, 3, 2, 2, 1, 0, -1, -2, -2, -3, -3, -4, -3, -3, -2, -2, -1, 0, 1, 2, 2, 3, 3, 4, 5, 4, 4, 3, 2, 1, 1, 0, 0, -1, -2, -3, -4, -4, -5, -6, -5, -4, -4, -3, -2, -1, -1, 0, 0, 1, 2, 3, 4, 4, 5, 6, 6, 5, 5, 5, 4

Offset: 0

Author

Hugo Pfoertner, Jan 06 2024

Keywords

• sign

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..3000
• Hugo Pfoertner, Plot of mapped spiral, using Plot 2.
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

A368123 gives the corresponding y-coordinates.

Cf. A367150, A368121, A368127, A368128.

Analogous pair of sequences, but without symmetrization: A367895, A367896.

Programs

PARI

\\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923.
\\ It is assumed that the PARI programs from A367150 and A368121 have been loaded and the functions defined there are available.
ax(n) = {my (m=sqrtint(n), k=ceil(m/2)); n -= 4*k^2; if (n<0, if (n<-m, k, -k-n), if (n