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 A318050 #24 Apr 06 2025 07:40:46 %S A318050 0,1,0,1,0,1,1,0,3,0,3,3,1,0,9,11,1,0,17,22,9,1 %N A318050 Triangle read by rows: T(n,k) is the number of prime knots with n crossings whose unknotting numbers are k. %C A318050 The unknotting number of a knot is the minimal number of crossing switches required to convert a knot into the unknot (0 crossing). %C A318050 Row n is a partition of A002863(n). %C A318050 Row 10 cannot yet be completed because the unknotting number of some knots are still unknown. %D A318050 P. R. Cromwell, Knots and Links, Cambridge University Press, 2004, pp. 151-154. %H A318050 S. A. Bleiler, <a href="http://dx.doi.org/10.1017/S0305004100062381">A note on unknotting number</a>, Math. Proc. Camb. Phil. Soc. Vol. 96 (1984). %H A318050 M. Borodzik and S. Friedl, <a href="http://dx.doi.org/10.2140/agt.2015.15.85">The unknotting number and classical invariants, I</a>, Algebraic and Geometric Topology Vol. 15 (2015), 85-135. %H A318050 J. C. Cha and C. Livingston, <a href="https://knotinfo.math.indiana.edu/">KnotInfo: Table of Knot Invariants</a>. %H A318050 S. Jablan and L. Radovic, <a href="http://elib.mi.sanu.ac.rs/files/journals/publ/115/n109p087.pdf">Unknotting numbers of alternating knot and link families</a>, Publications de l'Institut Mathématiques, Nouvelle série, tome 95 (2014), 87-99. %H A318050 K. Murasugi, <a href="http://dx.doi.org/10.2307/1994215">On a certain numerical invariant of link types</a>, Trans. Am. Math. Soc. Vol. 117 (1965), 387-422. %H A318050 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnknottingNumber.html">Unknotting Number</a>. %H A318050 <a href="/index/K#knots">Index entries for sequences related to knots</a> %e A318050 Triangle begins: %e A318050 n\k| 0 1 2 3 4 %e A318050 ---+------------------- %e A318050 3 | 0 1 %e A318050 4 | 0 1 %e A318050 5 | 0 1 1 %e A318050 6 | 0 3 %e A318050 7 | 0 3 3 1 %e A318050 8 | 0 9 11 1 %e A318050 9 | 0 17 22 9 1 %Y A318050 Cf. A002863, A078477, A089797, A089891, A089892, A173466, A318051, A318052. %K A318050 nonn,hard,more,tabf %O A318050 3,9 %A A318050 _Franck Maminirina Ramaharo_, Aug 14 2018