cp's OEIS Frontend

A127402 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.

%I A127402 #12 Oct 08 2017 12:27:40
%S A127402 0,6,6,12,12,24,24,42,54,60,72,84,96,126,138,156,168,204,204,246,270,
%T A127402 288,312,348,372,414,450,480,504,552,564,618,666,696,744,780,816,870,
%U A127402 930,960,1008,1080,1104,1182,1218,1272,1320,1392,1440,1506,1578,1632
%N A127402 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 A127402 Andrew Howroyd, <a href="/A127402/b127402.txt">Table of n, a(n) for n = 1..500</a>
%F A127402 a(n) = 2*(A053416(n) - A127403(n)). - _Andrew Howroyd_, Sep 16 2017
%e A127402 a(2)=6 because a disk of diameter 2 covers the 6 net points surrounding the deep hole.
%t A127402 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 A127402 Array[a, 52] (* _Jean-François Alcover_, Oct 08 2017, after _Andrew Howroyd_ *)
%o A127402 (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 A127402 Cf. A127403, A127404, A127405, A127406. The corresponding sequences for the square lattice and hexagonal lattice are A053415 and A053479, respectively.
%K A127402 nonn
%O A127402 1,2
%A A127402 _Hugo Pfoertner_, Feb 08 2007
%E A127402 Terms a(23) and beyond from _Andrew Howroyd_, Sep 16 2017