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 A011975 #32 Jan 10 2024 20:13:00
%S A011975 1,3,4,6,7,11,12,17,19,24,26,33,35,43,46,54,57,67,70,81,85,96,100,113,
%T A011975 117,131,136,150,155,171,176,193,199,216,222,241,247,267,274,294,301,
%U A011975 323,330,353,361,384,392,417,425,451,460,486
%N A011975 Covering numbers C(n,3,2).
%C A011975 Also, minimal number of triangles needed to cover every edge (and node) of a complete graph on n nodes. This problem is also known as the edge clique covering problem. - _Dmitry Kamenetsky_, Jan 24 2016
%D A011975 P. J. Cameron, Combinatorics, ..., Cambridge, 1994, see p. 121.
%D A011975 CRC Handbook of Combinatorial Designs, 1996, p. 262.
%D A011975 W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of Jeffrey H. Dinitz and D. R. Stinson, editors, Contemporary Design Theory, Wiley, 1992.
%H A011975 T. D. Noe, <a href="/A011975/b011975.txt">Table of n, a(n) for n = 3..1000</a>
%H A011975 Marek Cygan, Marcin Pilipczuk and Michał Pilipczuk, <a href="http://arxiv.org/abs/1203.1754">Known algorithms for EDGE CLIQUE COVER are probably optimal</a>, arXiv:1203.1754 [cs.DS], 2012.
%H A011975 Oliver Goldschmidt, Dorit S. Hochbaum, Cor Hurkens and Gang Yu, <a href="http://riot.ieor.berkeley.edu/~dorit/pub/k-clique.ps">Approximation Algorithms for the k-Clique Covering Problem</a>, Journal of Discrete Mathematics, volume 9, issue 3, pages 492-509, 1995, doi: 10.1137/S089548019325232X.
%H A011975 D. Gordon, <a href="http://www.dmgordon.org/cover">La Jolla Repository of Coverings</a>
%H A011975 Jenö Lehel, <a href="http://dx.doi.org/10.1002/jgt.3190130312">The minimum number of triangles covering the edges of a graph</a>, Journal of Graph Theory, volume 13, issue 3, pages 369-384, 1989.
%H A011975 Uenal Mutlu (uenalm(AT)metronet.de), <a href="http://www.tuco.de/math1.htm">Tables of coverings</a>
%H A011975 Wikipedia, <a href="https://en.wikipedia.org/wiki/Clique_cover_problem">Clique Cover Problem</a>.
%H A011975 <a href="/index/Cor#covnum">Index entries for covering numbers</a>
%F A011975 Conjecture: G.f. ( -1-2*x-2*x^5+x^7+x^6-x^8 ) / ( (1+x+x^2)*(x^2-x+1)*(1+x)^2*(x-1)^3 ) with a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-6) - a(n-7) - a(n-8) + a(n-9). - _R. J. Mathar_, Aug 12 2012
%F A011975 a(n) = ceiling((n/3)*ceiling((n-1)/2)). - _Nathaniel Johnston_, Jan 10 2024
%p A011975 L := proc(v,k,t,l) local i,t1; t1 := l; for i from v-t+1 to v do t1 := ceil(t1*i/(i-(v-k))); od: t1; end; # gives Schoenheim bound L_l(v,k,t). Present sequence is L_1(n,3,2,1).
%t A011975 L[v_, k_, t_, m_] := Module[{t1 = m}, Do[t1 = Ceiling[t1*i/(i - (v - k))], {i, v - t + 1, v}]; t1]; Table[L[n, 3, 2, 1], {n, 3, 100}] (* _T. D. Noe_, Sep 28 2011 *)
%Y A011975 Cf. A011976, A011977, A001839. A column of A066010. Also a column of A036838.
%K A011975 nonn,easy
%O A011975 3,2
%A A011975 _N. J. A. Sloane_