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

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 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.

Crossrefs

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

Programs

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