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A059774 Consider the line segment in R^n from the origin to the point P=(1,2,3,...,n); let d = squared distance to this line from the closest point of Z^n (excluding the endpoints). Sequence gives d times P.P.

%I A059774 #19 Apr 21 2021 04:34:15
%S A059774 1,3,9,21,40,75,120,189,285,385,506,650,819,1015,1240,1496,1785,2109,
%T A059774 2470,2870,3311,3795,4324,4900,5525,6201,6930,7714,8555,9455,10416,
%U A059774 11440,12529,13685,14910,16206,17575,19019,20540,22140,23821,25585,27434,29370
%N A059774 Consider the line segment in R^n from the origin to the point P=(1,2,3,...,n); let d = squared distance to this line from the closest point of Z^n (excluding the endpoints). Sequence gives d times P.P.
%C A059774 P.P is given by A000330(n). For n >= 10, a(n) = A000330(n-1).
%C A059774 Officially these are just conjectures so far.
%H A059774 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 A059774 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 A059774 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>]
%Y A059774 Cf. A000330, A059804, A047896.
%K A059774 nonn,easy,nice
%O A059774 2,2
%A A059774 _N. J. A. Sloane_ and _Vinay Vaishampayan_, Feb 21 2001