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A086825 Number of knots (prime or composite) with n crossings. 8
1, 0, 0, 1, 1, 2, 5, 8, 26 (list; graph; refs; listen; history; text; internal format)
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
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
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
KEYWORD
nonn,more
AUTHOR
Steven Finch, Aug 07 2003
EXTENSIONS
a(8) corrected by Kyle Miller, Oct 14 2020
STATUS
approved

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Last modified February 24 05:45 EST 2024. Contains 370292 sequences. (Running on oeis4.)