A307016 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 second coordinate in a barycentric coordinate system.

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

Offset

0,9

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 j. i is given in A307014, k is given in A307017.

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..9060, covering range r <= 50.

Hugo Pfoertner, PARI program for A307014 and A307016.

Prog

(PARI) \\ See Link
\\ To create the data of this sequence load program from file and call
a307014_16(5, 6) \\ Hugo Pfoertner, Nov 07 2023

Crossrefs

Cf. A004016, A035019, A038590, A307014, A307017.

Sequence in context: A099075 A366835 A364312 * A143158 A336708 A308424

Adjacent sequences: A307013 A307014 A307015 * A307017 A307018 A307019

Keyword

sign,look

Author

Hugo Pfoertner, Mar 21 2019

Status

approved