A127402 - OEIS

%I #12 Oct 08 2017 12:27:40

%S 0,6,6,12,12,24,24,42,54,60,72,84,96,126,138,156,168,204,204,246,270,

%T 288,312,348,372,414,450,480,504,552,564,618,666,696,744,780,816,870,

%U 930,960,1008,1080,1104,1182,1218,1272,1320,1392,1440,1506,1578,1632

%N 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.

%H Andrew Howroyd, <a href="/A127402/b127402.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = 2*(A053416(n) - A127403(n)). - _Andrew Howroyd_, Sep 16 2017

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

%t a[n_] := Sum[Boole[4*(i^2 + i*j + j^2) <= n^2 && Mod[i - j, 3] != 0], {i, -n, n}, {j, -n, n}];

%t Array[a, 52] (* _Jean-François Alcover_, Oct 08 2017, after _Andrew Howroyd_ *)

%o (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

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

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Feb 08 2007

%E Terms a(23) and beyond from _Andrew Howroyd_, Sep 16 2017