cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

1, 0, 0, 1, 1, 2, 5, 8, 26
Offset: 0

Views

Author

Steven Finch, Aug 07 2003

Keywords

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

Examples

			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).

Links

Crossrefs

Cf. A002863 (prime knots), A227050, A086826.
A283314 gives the partial sums.

Extensions

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

A283315 Total number of nontrivial knots (prime or composite) with <= n crossings.

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 9, 17, 43
Offset: 0

Views

Author

N. J. A. Sloane, Mar 08 2017, following a suggestion from Daniel Forgues

Keywords

Crossrefs

Equals A283314(n) - 1.

Extensions

a(8) corrected from A086825 by Kyle Miller, Oct 14 2020
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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