A070263 - OEIS

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A070263

Triangle T(n,k), n >= 0, 1 <= k <= 2^n, read by rows, giving minimal distance-sum of any set of k binary vectors of length n.

0, 0, 1, 0, 1, 4, 8, 0, 1, 4, 8, 16, 25, 36, 48, 0, 1, 4, 8, 16, 25, 36, 48, 68, 89, 112, 136, 164, 193, 224, 256, 0, 1, 4, 8, 16, 25, 36, 48, 68, 89, 112, 136, 164, 193, 224, 256, 304, 353, 404, 456, 512, 569, 628, 688, 756, 825, 896, 968, 1044, 1121, 1200, 1280

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OFFSET

0,6

COMMENTS

For n >= 8 the rows have different beginnings.

LINKS

Table of n, a(n) for n=0..62.

A. Kündgen, Minimum average distance subsets in the Hamming cube, Discrete Math., 249 (2002), 149-165.

FORMULA

Rows seem to converge to expansion of (1/(1-x)^2) * Sum_{k>=0} 2^k*t/(1-t^2), where t = x^2^k. - Ralf Stephan, Sep 12 2003

EXAMPLE

0; 0,1; 0,1,4,8; 0,1,4,8,16,25,36,48; 0,1,4,8,16,25,36,48,68,89,112,...