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A018240 Rational knots with n crossings (up to mirroring). 5
1, 1, 2, 3, 7, 12, 24, 45, 91, 176, 352, 693, 1387, 2752 (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

Table of n, a(n) for n=3..16.

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

CROSSREFS

Cf. A090596.

Sequence in context: A000630 A036538 A108742 * A090596 A054272 A129016

Adjacent sequences:  A018237 A018238 A018239 * A018241 A018242 A018243

KEYWORD

nice,more,nonn

AUTHOR

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

STATUS

approved

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Last modified December 22 20:35 EST 2014. Contains 252372 sequences.