A127402 Number of points in a honeycomb net covered by a circular disk of diameter n if the center of the circle is chosen at the deep hole.

0, 6, 6, 12, 12, 24, 24, 42, 54, 60, 72, 84, 96, 126, 138, 156, 168, 204, 204, 246, 270, 288, 312, 348, 372, 414, 450, 480, 504, 552, 564, 618, 666, 696, 744, 780, 816, 870, 930, 960, 1008, 1080, 1104, 1182, 1218, 1272, 1320, 1392, 1440, 1506, 1578, 1632

Offset: 1

Author

Hugo Pfoertner, Feb 08 2007

Keywords

• nonn

Examples

			a(2)=6 because a disk of diameter 2 covers the 6 net points surrounding the deep hole.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A127403, A127404, A127405, A127406. The corresponding sequences for the square lattice and hexagonal lattice are A053415 and A053479, respectively.

Programs

Mathematica

a[n_] := Sum[Boole[4*(i^2 + i*j + j^2) <= n^2 && Mod[i - j, 3] != 0], {i, -n, n}, {j, -n, n}];
Array[a, 52] (* Jean-François Alcover, Oct 08 2017, after Andrew Howroyd *)

PARI

a(n) = sum(i=-n, n, sum(j=-n, n, 4*(i^2 + i*j + j^2) <= n^2 && (i-j) % 3 != 0)); \\ Andrew Howroyd, Sep 16 2017

Formula

a(n) = 2*(A053416(n) - A127403(n)). - Andrew Howroyd, Sep 16 2017

Extensions

Terms a(23) and beyond from Andrew Howroyd, Sep 16 2017