A230014 Triangle E(n,k), 1<=k<=n, giving the cardinality of optimal binary covering codes of empty spheres of length n and radius k.

2, 2, 4, 4, 4, 8, 4, 4, 4, 16, 8, 6, 6, 8, 32, 14, 8, 6, 8, 14, 64, 24, 8, 8, 8, 8, 24, 128, 32, 16, 8, 8, 8, 16, 32, 256, 64, 24, 12, 10, 10, 12, 24, 64, 512, 124

Offset: 1

Author

Kamiel P.F. Verstraten, Feb 22 2014

Keywords

• nonn
• hard
• more
• tabl

Comments

The next term is in the range 34-40.

Note that E(n,k) = E(n,n-k).

Examples

			Triangle starts:
01: 2,
02: 2, 4,
03: 4, 4, 8,
04: 4, 4, 4, 16,
05: 8, 6, 6, 8, 32,
06: 14, 8, 6, 8, 14, 64,
07: 24, 8, 8, 8, 8, 24, 128,
08: 32, 16, 8, 8, 8, 16, 32, 256,
09: 64, 24, 12, 10, 10, 12, 24, 64, 512,
10: 124, ...
		

Links

• Kamiel P. F. Verstraten, A Generalization of the Football Pool Problem, Master's Thesis, Tilburg University, 2014

Crossrefs

Related to A060438, which has a code consisting of filled spheres instead of empty spheres.

Related to A238305, the triangle giving the cardinality of optimal ternary covering codes of empty spheres.

The first column is equal to 2*A000983.

Extensions

a(43) corrected by Omar E. Pol, Nov 23 2014