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Squared radii of circles which exactly encircle clusters in the A2 lattice in increasing order.
1

%I #11 May 12 2014 11:52:44

%S 0,4,9,13,21,25,28,36,39,43,49,57,63,64,67,76,81,84,91,93,97,109,111,

%T 117,121,124,129,133,144,147,148,156,157,163,171,175,183,189,193,196,

%U 199,201

%N Squared radii of circles which exactly encircle clusters in the A2 lattice in increasing order.

%H Rajan Murthy, <a href="/A240692/a240692.txt">Generating code for the sequence (Scilab)</a>

%e For n = 1, a(1) = 4, the squared distance to the corners furthest from the deep hole of three hexagons which share the deep hole as a corner.

%e For n= 3, a(3) = 13, the squared distance to the furthest corners of the 6 hexagons third most distant from the deep hole - which, when added to the 3 that are closest and the 3 that are second-closest, yields a total of 12, which is A038588(3).

%Y A038588(n) gives the corresponding cluster size starting at n = 1 (the first positive radius circle);

%Y A000404 is the analog for a Cartesian lattice.

%K nonn

%O 0,2

%A _Rajan Murthy_, Apr 10 2014