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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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]

MATHEMATICA

a[n_] := If[n<10, {1, 3, 9, 21, 40, 75, 120, 189}[[n-1]], n(n-1)(2n-1)/6]; Table[a[n], {n, 2, 45}] (* Jean-Fran├žois Alcover, Feb 29 2016, from conjectural formula *)

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

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Last modified December 4 11:13 EST 2016. Contains 278750 sequences.