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 A086825 #38 Feb 16 2025 08:32:50 %S A086825 1,0,0,1,1,2,5,8,26 %N A086825 Number of knots (prime or composite) with n crossings. %C A086825 For n = 0, we have the trivial knot (the unknot), which is neither a prime knot nor a composite knot. - _Daniel Forgues_, Feb 12 2016 %H A086825 S. R. Finch, <a href="/A002863/a002863_4.pdf">Knots, links and tangles</a>, August 8, 2003. [Cached copy, with permission of the author] %H A086825 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Knot.html">Knot</a> %H A086825 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Unknot.html">Unknot</a> %H A086825 <a href="/index/K#knots">Index entries for sequences related to knots</a> %e A086825 a(7)=8 since we have 7 prime knots and one composite knot (the connected sum 3_1#4_1 of the trefoil knot 3_1 and the figure eight knot 4_1). Note that 3_1*#4_1=3_1#4_1, where * denotes mirror image because 4_1 is achiral. %e A086825 a(8)=26 since we have 21 prime knots and five composites (3_1#5_1, 3_1#5_2, 3_1*#5_1, 3_1*#5_2, and 4_1#4_1). %Y A086825 Cf. A002863 (prime knots), A227050, A086826. %Y A086825 A283314 gives the partial sums. %K A086825 nonn,more %O A086825 0,6 %A A086825 _Steven Finch_, Aug 07 2003 %E A086825 a(8) corrected by _Kyle Miller_, Oct 14 2020