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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A315783 A315784 A315785 * A161418 A124691 A315786

Adjacent sequences: A127399 A127400 A127401 * A127403 A127404 A127405

Keyword

nonn

Author

Hugo Pfoertner, Feb 08 2007

Extensions

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

Status

approved