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A086826
Number of nonsplittable links (prime or composite) with n crossings.
2
1, 0, 1, 1, 3, 4, 15, 24, 82
OFFSET
0,5
COMMENTS
A link L is splittable if we can embed a plane in R^3, disjoint from L, that separates one or more components of L from other components of L. Otherwise L is nonsplittable.
LINKS
S. R. Finch, Knots, links and tangles, August 8, 2003. [Cached copy, with permission of the author]
Stéphane Legendre, Table of nonsplittable links
Eric Weisstein's World of Mathematics, Splittable Link
EXAMPLE
a(5)=4 since we have 2 prime knots, as well as the Whitehead link; and the trefoil knot linked with a circle.
a(6)=15 since we have 3 prime knots, as well as 2 composite knots (the square & granny knots); 6 prime links; a chain of four circles simply-intertwined; four circles simply-intertwined in the shape of a "T"; three circles, two doubly-intertwined and two simply-intertwined; and the figure-eight knot linked with a circle.
CROSSREFS
Sequence in context: A286025 A286645 A290863 * A081405 A167367 A024858
KEYWORD
nonn
AUTHOR
Steven Finch, Aug 07 2003
EXTENSIONS
a(7) and a(8) from Stéphane Legendre, Jan 06 2014
STATUS
approved