%I #19 Apr 21 2021 04:34:15

%S 1,3,9,21,40,75,120,189,285,385,506,650,819,1015,1240,1496,1785,2109,

%T 2470,2870,3311,3795,4324,4900,5525,6201,6930,7714,8555,9455,10416,

%U 11440,12529,13685,14910,16206,17575,19019,20540,22140,23821,25585,27434,29370

%N 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 P.P is given by A000330(n). For n >= 10, a(n) = A000330(n-1).

%C Officially these are just conjectures so far.

%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>]

%Y Cf. A000330, A059804, A047896.

%K nonn,easy,nice

%O 2,2

%A _N. J. A. Sloane_ and _Vinay Vaishampayan_, Feb 21 2001