cp's OEIS Frontend

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.

%I A307014 #18 Nov 07 2023 14:35:41
%S A307014 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,
%T A307014 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,
%U A307014 -4,-4,0,4,3,2,-2,-3,-5,-5,-3,-2,2,3,5,5,4,1
%N 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.
%C A307014 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.
%C A307014 The sorting by polar angle affects the grid points in the shells of size A035019, starting at indices given by A038590.
%H A307014 Hugo Pfoertner, <a href="/A307014/b307014.txt">Table of n, a(n) for n = 0..9060</a>, covering range r <= 50.
%H A307014 Hugo Pfoertner, <a href="/A307014/a307014.pdf">Illustration of initial terms of A307014 and A307016</a>.
%H A307014 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A307014&amp;name2=A307016&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=xy&amp;drawpoints=true">Illustration of A307016 vs A307014</a>, grid points.
%H A307014 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A307014&amp;name2=A307016&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=xy&amp;drawlines=true">Illustration of A307016 vs A307014</a>, spiral.
%H A307014 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A307014&amp;name2=A307017&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=xy&amp;drawlines=true">Illustration of A307017 vs A307014</a>, spiral.
%H A307014 Hugo Pfoertner, <a href="/A307014/a307014.gp.txt">PARI program for A307014 and A307016</a>.
%o A307014 (PARI) \\ See Link
%o A307014 \\ To create the data of this sequence load program from file and call
%o A307014 a307014_16(5, 4) \\ _Hugo Pfoertner_, Nov 07 2023
%Y A307014 Cf. A004016, A035019, A038590, A305575, A305576, A307011, A307012, A307013, A307016, A307017.
%K A307014 sign,look
%O A307014 0,10
%A A307014 _Hugo Pfoertner_, Mar 21 2019