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

0,3

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A353615 A088838 A367688 * A276423 A052993 A214779

Adjacent sequences: A127400 A127401 A127402 * A127404 A127405 A127406

Keyword

nonn

Author

Hugo Pfoertner, Feb 08 2007

Extensions

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

Status

approved