A086825 Number of knots (prime or composite) with n crossings.

1, 0, 0, 1, 1, 2, 5, 8, 26

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