

A086825


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


7




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

Table of n, a(n) for n=0..8.
S. R. Finch, Knots, links and tangles, August 8, 2003. [Cached copy, with permission of the author]
Eric Weisstein's World of Mathematics, Knot
Eric Weisstein's World of Mathematics, Unknot
Index entries for sequences related to knots


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

Cf. A002863 (prime knots), A227050, A086826.
A283314 gives the partial sums.
Sequence in context: A100501 A291605 A142869 * A192476 A093365 A209865
Adjacent sequences: A086822 A086823 A086824 * A086826 A086827 A086828


KEYWORD

nonn,more


AUTHOR

Steven Finch, Aug 07 2003


EXTENSIONS

a(8) corrected by Kyle Miller, Oct 14 2020


STATUS

approved



