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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.
8
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
0,10
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 A307016 vs A307014, grid points.
Hugo Pfoertner, Illustration of A307016 vs A307014, spiral.
Hugo Pfoertner, Illustration of A307017 vs A307014, spiral.
PROG
(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
KEYWORD
sign,look
AUTHOR
Hugo Pfoertner, Mar 21 2019
STATUS
approved