A127403 Number of points in a honeycomb net covered by a circular disk of diameter n if the center of the circle is chosen at a grid point.

1, 1, 4, 4, 13, 13, 25, 31, 40, 46, 61, 73, 85, 103, 124, 130, 163, 169, 199, 211, 244, 262, 295, 319, 343, 385, 406, 436, 481, 505, 547, 577, 622, 646, 697, 739, 775, 829, 868, 916, 979, 1015, 1075, 1111, 1174, 1204, 1285, 1333, 1387, 1453, 1510, 1558, 1639

Offset: 0

Author

Hugo Pfoertner, Feb 08 2007

Keywords

• nonn

Examples

			a(2)=4 because a disk of diameter 2 covers the center of the circle and the 3 net points at distance 1.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A127402, A127404, A127405, A127406. The corresponding sequences for the square lattice and hexagonal lattice are A053411 and A053416, respectively.

Programs

Mathematica

a[n_] := Sum[Boole[4*(i^2 + i*j + j^2) <= n^2 && Mod[i - j , 3] != 1], {i, -n, n}, {j, -n, n}];
Table[a[n], {n, 0, 52}] (* Jean-François Alcover, Oct 08 2017, translated from PARI *)

PARI

a(n) = sum(i=-n, n, sum(j=-n, n, 4*(i^2 + i*j + j^2) <= n^2 && (i-j) % 3 != 1)); \\ Andrew Howroyd, Sep 16 2017

Extensions

a(0) and terms a(23) and beyond from Andrew Howroyd, Sep 16 2017