

A086825


Number of knots (prime or composite) with n crossings.


8




OFFSET

0,6


COMMENTS

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


LINKS

Eric Weisstein's World of Mathematics, Knot
Eric Weisstein's World of Mathematics, Unknot


EXAMPLE

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)=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).


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



