cp's OEIS Frontend

A125852 Number of points in a hexagonal lattice covered by a circular disk of diameter n if the center of the circle is chosen such that the disk covers the maximum possible number of lattice points.

%I A125852 #9 Mar 31 2012 14:12:21
%S A125852 2,7,10,19,24,37,48,61,77,94,115,134,157,187,208,241,265,301,330,367,
%T A125852 406,444,486,527,572,617,665,721,769,825,877,935,993,1054,1117,1182,
%U A125852 1249,1316,1385,1459,1531,1615,1684,1765,1842,1925,2011,2096,2187,2276
%N A125852 Number of points in a hexagonal lattice covered by a circular disk of diameter n if the center of the circle is chosen such that the disk covers the maximum possible number of lattice points.
%C A125852 a(n)>=max(A053416(n),A053479(n),A053417(n)). a(n) is an upper bound for the number of segments of a self avoiding path on the 2-dimensional triangular lattice such that the path fits into a circle of diameter n. A122226(n)<=a(n).
%H A125852 H. v. Eitzen, <a href="/A125852/b125852.txt">Table of n, a(n) for n=1..1000</a>
%H A125852 <a href="/index/Aa#A2">Index entries for sequences related to A2 = hexagonal = triangular lattice</a>
%H A125852 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a125852.pdf">Maximum number of points in the hexagonal lattice covered by circular disks.</a> Illustrations.
%Y A125852 Cf. A053416, A053479, A053417, A125851, A122226. The corresponding sequences for the square lattice and the honeycomb net are A123690 and A127406, respectively.
%K A125852 nonn
%O A125852 1,1
%A A125852 _Hugo Pfoertner_, Jan 07 2007, Feb 11 2007
%E A125852 More terms copied from b-file by _Hagen von Eitzen_, Jun 17 2009