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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,3 COMMENTS Identical through a(13) = 352 with Two-bridge Knots of crossing number n, in Table 1: Number of knots having two-bridged Conway polynomials, of Koseleff. There is a conjecture that this is the same as A090596. LINKS C. Ernst and D. W. Sumners, The Growth of the Number of Prime Knots, Math. Proc. Cambridge Philos. Soc. 102, 303-315, 1987. P. -V. Koseleff, D. Pecker, Conway polynomials of two-bridge links, arXiv:1011.5992 [math.GT], 2010. FORMULA Empirical g.f.: -x^3*(x^4+x^3+2*x^2-1) / ((x+1)*(2*x-1)*(x^2+1)*(2*x^2-1)). - 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 A298897 A054272 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

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Last modified March 23 04:45 EDT 2018. Contains 301099 sequences. (Running on oeis4.)