cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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.

Original entry on oeis.org

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

Views

Author

Kamiel P.F. Verstraten, Feb 22 2014

Keywords

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, ...
		

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

A247181 Total domination number of the n-hypercube graph.

Original entry on oeis.org

2, 2, 4, 4, 8, 14, 24, 32, 64, 124
Offset: 1

Views

Author

Jernej Azarija, Nov 22 2014

Keywords

Comments

a(n) = size of smallest subset S of vertices of the n-cube Q_n such that every vertex of Q_n has a neighbor in S.
Proof for first formula can be found in the Verstraten link. - Kamiel P.F. Verstraten, Jun 10 2015

Examples

			a(1) = 2 since the complete graph on two vertices can only be totally dominated by taking both vertices.
		

Crossrefs

Cf. A000983 (half), A323515 (number of sets).

Formula

a(n) = 2*A000983(n-1), at least if 2<=n<=9. - Omar E. Pol, Nov 22 2014. This formula is true for all n>=2 (see Azarija-Henning-Klavžar paper). - Omar E. Pol, Jul 01 2016
a(n) = A230014(n,1), at least if 1<=n<=9. - Omar E. Pol, Nov 23 2014. This formula is true for all n>=1 (in accordance with the above comment). - Omar E. Pol, Jul 01 2016

Extensions

a(10) from Jernej Azarija, Jun 30 2016
Showing 1-2 of 2 results.