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%I #37 Oct 14 2020 23:13:29
%S 1,0,0,1,1,2,5,8,26
%N Number of knots (prime or composite) with n crossings.
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Knot.html">Knot</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Unknot.html">Unknot</a>
%H <a href="/index/K#knots">Index entries for sequences related to knots</a>
%e 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 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 Cf. A002863 (prime knots), A227050, A086826.
%Y A283314 gives the partial sums.
%K nonn,more
%O 0,6
%A _Steven Finch_, Aug 07 2003
%E a(8) corrected by _Kyle Miller_, Oct 14 2020
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