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

Offset: 0

Author

Andre Kundgen (akundgen(AT)csusm.edu), May 09 2002

Keywords

• nonn
• tabf

Comments

For n >= 8 the rows have different beginnings.

Examples

			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,...
		

Links

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

Crossrefs

Cf. A022560.

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

Extensions

More terms from Sean A. Irvine, Jun 06 2024