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

1,1

Comments

The next term is in the range 34-40.

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

Links

Table of n, a(n) for n=1..46.

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

Example

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, ...

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.

Sequence in context: A305586 A305040 A316693 * A319414 A303961 A305340

Adjacent sequences: A230011 A230012 A230013 * A230015 A230016 A230017

Keyword

nonn,hard,more,tabl

Author

Kamiel P.F. Verstraten, Feb 22 2014

Extensions

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

Status

approved