

A018240


Rational knots with n crossings (up to mirroring).


6



1, 1, 2, 3, 7, 12, 24, 45, 91, 176, 352, 693, 1387, 2752, 5504, 10965, 21931, 43776, 87552, 174933, 349867, 699392
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OFFSET

3,3


COMMENTS

Identical through a(13) = 352 with Twobridge Knots of crossing number n, in Table 1: Number of knots having twobridged Conway polynomials, of Koseleff.
There is a conjecture that this is the same as A090596.


LINKS

Table of n, a(n) for n=3..24.
C. Ernst and D. W. Sumners, The Growth of the Number of Prime Knots, Math. Proc. Cambridge Philos. Soc. 102, 303315, 1987.
P. V. Koseleff, D. Pecker, Conway polynomials of twobridge links, arXiv:1011.5992 [math.GT], 2010.


FORMULA

Empirical g.f.: x^3*(x^4+x^3+2*x^21) / ((x+1)*(2*x1)*(x^2+1)*(2*x^21)).  Colin Barker, Oct 07 2014


EXAMPLE

The a(7)=7 rational knots with 7 crossings are 7, 52, 43, 322, 313, 2212, 21112. All the rational knots are listed in A122495.


CROSSREFS

Cf. A090596, A122495, A005418, A002863, A086825, A089790.
Sequence in context: A000630 A036538 A108742 * A090596 A321838 A298897
Adjacent sequences: A018237 A018238 A018239 * A018241 A018242 A018243


KEYWORD

nice,more,nonn


AUTHOR

Alexander Stoimenow (stoimeno(AT)math.toronto.edu)


EXTENSIONS

a(17)a(24) from Andrey Zabolotskiy, Feb 09 2018


STATUS

approved



