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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: 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

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Last modified August 20 08:21 EDT 2019. Contains 326143 sequences. (Running on oeis4.)