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

2,2

Comments

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

Officially these are just conjectures so far.

Links

Table of n, a(n) for n=2..45.

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.

Sequence in context: A112039 A007518 A029494 * A064999 A100135 A024173

Adjacent sequences: A059771 A059772 A059773 * A059775 A059776 A059777

Keyword

nonn,easy,nice

Author

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

Status

approved