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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 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

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