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.

1, 3, 9, 21, 40, 75, 120, 189, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201, 6930, 7714, 8555, 9455, 10416, 11440, 12529, 13685, 14910, 16206, 17575, 19019, 20540, 22140, 23821, 25585, 27434, 29370

Offset: 2

Author

N. J. A. Sloane and Vinay Vaishampayan, Feb 21 2001

Keywords

• nonn
• easy
• nice

Comments

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

Officially these are just conjectures so far.

Links

• N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, Fat Struts: Constructions and a Bound, Proceedings Information Theory Workshop, Taormino, Italy, 2009. [Cached copy]
• N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, A Note on Projecting the Cubic Lattice, Discrete and Computational Geometry, Vol. 46 (No. 3, 2011), 472-478.
• N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, The Lifting Construction: A General Solution to the Fat Strut Problem, Proceedings International Symposium on Information Theory (ISIT), 2010, IEEE Press. [Cached copy]

Crossrefs

Cf. A000330, A059804, A047896.