cp's OEIS Frontend

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.

%I A127403 #11 Oct 08 2017 10:41:03
%S A127403 1,1,4,4,13,13,25,31,40,46,61,73,85,103,124,130,163,169,199,211,244,
%T A127403 262,295,319,343,385,406,436,481,505,547,577,622,646,697,739,775,829,
%U A127403 868,916,979,1015,1075,1111,1174,1204,1285,1333,1387,1453,1510,1558,1639
%N 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.
%H A127403 Andrew Howroyd, <a href="/A127403/b127403.txt">Table of n, a(n) for n = 0..500</a>
%e A127403 a(2)=4 because a disk of diameter 2 covers the center of the circle and the 3 net points at distance 1.
%t A127403 a[n_] := Sum[Boole[4*(i^2 + i*j + j^2) <= n^2 && Mod[i - j , 3] != 1], {i, -n, n}, {j, -n, n}];
%t A127403 Table[a[n], {n, 0, 52}] (* _Jean-François Alcover_, Oct 08 2017, translated from PARI *)
%o A127403 (PARI)
%o A127403 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
%Y A127403 Cf. A127402, A127404, A127405, A127406. The corresponding sequences for the square lattice and hexagonal lattice are A053411 and A053416, respectively.
%K A127403 nonn
%O A127403 0,3
%A A127403 _Hugo Pfoertner_, Feb 08 2007
%E A127403 a(0) and terms a(23) and beyond from _Andrew Howroyd_, Sep 16 2017