%I A086825
%S A086825 1,0,0,1,1,2,5,8,25
%N A086825 Number of knots (prime or composite) with n crossings.
%H A086825 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Knots, links and 
               tangles</a>
%H A086825 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Knot.html">Knot</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. a(8)=25 since we have 21 prime knots and four composites 
               (3_1#5_1, 3_1#5_2, 3_1*#5_1 and 3_1*#5_2).
%Y A086825 Cf. A002863.
%Y A086825 Sequence in context: A088144 A100501 A142869 this_sequence A093365 A128600 
               A066846
%Y A086825 Adjacent sequences: A086822 A086823 A086824 this_sequence A086826 A086827 
               A086828
%K A086825 nonn
%O A086825 0,6
%A A086825 S. R. Finch (Steven.Finch(AT)inria.fr), Aug 07 2003