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%I #18 Mar 25 2015 16:29:06
%S 1,1,2,3,1,2,3,0,2,4,2,3,3,3,5,0,2,5,3,4,5,6,5,0,6,4,5,3,5,9,6,0,6,8,
%T 6,8,9,8,9,0,5,6,5,8,9,11,10,0,6,11,9,4,10,11,10,0,14,9,11,11,9,11,14,
%U 0,14,11,11,8,11,19,14,0,9,11,11,8,10,14,14,0,14,10,13,20,21
%N For given n, consider all 4-tuples P = (a,b,c,d) with P.P = n; let d = squared distance to the line OP from the closest point of Z^n (excluding the endpoints); sequence gives max_P d*n.
%C A form of generalized GCD of 4 numbers.
%H N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/Exists.pdf">Fat Struts: Constructions and a Bound</a>, Proceedings Information Theory Workshop, Taormino, Italy, 2009. [<a href="/A047896/a047896.pdf">Cached copy</a>]
%H N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/FATS.pdf">A Note on Projecting the Cubic Lattice</a>, Discrete and Computational Geometry, Vol. 46 (No. 3, 2011), 472-478.
%H N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/main_fat_strut.pdf">The Lifting Construction: A General Solution to the Fat Strut Problem</a>, Proceedings International Symposium on Information Theory (ISIT), 2010, IEEE Press. [<a href="/A047896/a047896_1.pdf">Cached copy</a>]
%e n=10, best P is (1,1,2,2), closest point of Z^4 to OP is (0,0,1,1) at squared distance d = 2/5, so a(10) = 10*2/5 = 4.
%Y Cf. A059804, A059774.
%K nonn
%O 1,3
%A _N. J. A. Sloane_ and _Vinay Vaishampayan_, Feb 27 2001
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