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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

%I #28 Jun 18 2015 10:10:44

%S 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,

%T 16,8,8,8,16,32,256,64,24,12,10,10,12,24,64,512,124

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

%C The next term is in the range 34-40.

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

%H Kamiel P. F. Verstraten, <a href="https://oeis.org/A238305/a238305.pdf">A Generalization of the Football Pool Problem</a>, Master's Thesis, Tilburg University, 2014

%e Triangle starts:

%e 01: 2,

%e 02: 2, 4,

%e 03: 4, 4, 8,

%e 04: 4, 4, 4, 16,

%e 05: 8, 6, 6, 8, 32,

%e 06: 14, 8, 6, 8, 14, 64,

%e 07: 24, 8, 8, 8, 8, 24, 128,

%e 08: 32, 16, 8, 8, 8, 16, 32, 256,

%e 09: 64, 24, 12, 10, 10, 12, 24, 64, 512,

%e 10: 124, ...

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

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

%Y The first column is equal to 2*A000983.

%K nonn,hard,more,tabl

%O 1,1

%A _Kamiel P.F. Verstraten_, Feb 22 2014

%E a(43) corrected by _Omar E. Pol_, Nov 23 2014