A060454 Consider the line segment in R^n from the origin to the point v = (1,4,9,...,n^2); let d = squared distance to this line from the closest point of Z^n (excluding the endpoints). Sequence gives d times v.v.

1, 6, 38, 107, 350, 728, 1752, 3090, 6215, 9878, 17654, 26117, 42924, 60256, 93024, 125460, 184509, 241110, 341110, 434511, 595562, 742808, 991640, 1215110, 1586403, 1914822, 2452646, 2922185, 3681560, 4337024, 5385600, 6281704, 7701561, 8904294, 10793862, 12381939, 14822755, 16907891, 19221332, 21781332, 24607093, 27718789, 31137590

Offset

0,2

Comments

v.v is given by A000538(n).

Officially these are just conjectures so far.

Links

Table of n, a(n) for n=0..42.

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]

Formula

For n<=37, a(n) = A060452(n); for n >= 38, a(n) = A000538(n-1).

Crossrefs

Cf. A059804.

Sequence in context: A216384 A360739 A352305 * A060452 A229620 A045949

Adjacent sequences: A060451 A060452 A060453 * A060455 A060456 A060457

Keyword

nonn

Author

N. J. A. Sloane, Apr 09 2001

Status

approved