A307014 List coordinates (x,y) of the points in an hexagonal grid, sorted first by radial coordinate r and in case of ties, by polar angle 0 <= phi < 2*Pi in a polar coordinate system. Sequence gives the first coordinate in a barycentric coordinate system.

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

Offset: 0

Author

Hugo Pfoertner, Mar 21 2019

Keywords

• sign
• look

Comments

Cartesian coordinates (x,y) of the grid points are converted to barycentric coordinates (i,j,k) by i = x - y/sqrt(3), j = 2*y/sqrt(3), k = x + y/sqrt(3). The sequence gives i. j is given in A307016, k is given in A307017.

The sorting by polar angle affects the grid points in the shells of size A035019, starting at indices given by A038590.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..9060, covering range r <= 50.
• Hugo Pfoertner, Illustration of initial terms of A307014 and A307016.
• Hugo Pfoertner, Illustration of A307016 vs A307014, grid points.
• Hugo Pfoertner, Illustration of A307016 vs A307014, spiral.
• Hugo Pfoertner, Illustration of A307017 vs A307014, spiral.
• Hugo Pfoertner, PARI program for A307014 and A307016.

Crossrefs

Cf. A004016, A035019, A038590, A305575, A305576, A307011, A307012, A307013, A307016, A307017.

Programs

PARI

\\ See Link
\\ To create the data of this sequence load program from file and call
a307014_16(5, 4) \\ Hugo Pfoertner, Nov 07 2023