

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.


5



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
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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}] (* JeanFrançois 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 && (ij) % 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: A038804 A183362 A088838 * 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



