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.
%I A247181 #61 Feb 16 2025 08:33:23 %S A247181 2,2,4,4,8,14,24,32,64,124 %N A247181 Total domination number of the n-hypercube graph. %C A247181 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. %C A247181 Proof for first formula can be found in the Verstraten link. - _Kamiel P.F. Verstraten_, Jun 10 2015 %H A247181 J. Azarija, M. A. Henning and S. Klavžar <a href="http://arxiv.org/abs/1606.08143">(Total) Domination in Prisms</a>, arXiv:1606.08143 [math.CO], 2016. %H A247181 Jernej Azarija, S. Klavzar, Y. Rho, and S. Sim, <a href="https://www.fmf.uni-lj.si/~klavzar/preprints/Total-dom-cubes-submit.pdf">On domination-type invariants of Fibonacci cubes and hypercubes</a>, Preprint 2016; See Table 4. %H A247181 Jernej Azarija, S. Klavzar, Y. Rho, and S. Sim, <a href="https://amc-journal.eu/index.php/amc/article/view/1172">On domination-type invariants of Fibonacci cubes and hypercubes</a>, Ars Mathematica Contemporanea, 14 (2018) 387-395. See Table 4. %H A247181 M. Henning and A. Yeo, <a href="http://dx.doi.org/10.1007/978-1-4614-6525-6">Total domination in graphs</a>, Springer, 2013. %H A247181 Kamiel P. F. Verstraten, <a href="/A238305/a238305.pdf">A Generalization of the Football Pool Problem</a>, Master's Thesis, Tilburg University, 2014. %H A247181 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a> %H A247181 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominationNumber.html">Total Domination Number</a> %F A247181 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 %F A247181 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 %e A247181 a(1) = 2 since the complete graph on two vertices can only be totally dominated by taking both vertices. %Y A247181 Cf. A000983 (half), A323515 (number of sets). %K A247181 nonn,more,hard %O A247181 1,1 %A A247181 _Jernej Azarija_, Nov 22 2014 %E A247181 a(10) from _Jernej Azarija_, Jun 30 2016