login
Prime unoriented alternating links (not necessarily connected knots) with n crossings.
3

%I #21 Jun 09 2022 06:21:02

%S 0,1,1,2,3,8,14,39,96,297,915,3308,12417,51347,222595,1016975,4799520,

%T 23301779,115405815,581071711,2963793396,15283327150,79544488072,

%U 417377448058

%N Prime unoriented alternating links (not necessarily connected knots) with n crossings.

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Knots, links and tangles</a> [dead link]

%H S. R. Finch, <a href="/A002863/a002863_4.pdf">Knots, links and tangles</a>, Aug 08 2003. [Cached copy, with permission of the author]

%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 626.

%H Bruce Fontaine, <a href="https://pi.math.cornell.edu/~bfontain/knots.html">Knots/Links</a>

%H Stavros Garoufalidis and Thao Vuong, <a href="https://doi.org/10.1007/s11139-014-9592-5">Alternating knots, planar graphs, and q-series</a>, The Ramanujan Journal 36.3 (2015): 501-527; arXiv:<a href="https://arxiv.org/abs/1304.1071">1304.1071</a> [math.GT], 2013. See (28).

%Y Cf. A002864, A086771. Row sums of A059739.

%K nonn,nice,hard,more

%O 1,4

%A _N. J. A. Sloane_, Feb 10 2001

%E a(20)-a(24) from Bruce Fontaine's table (produced by him together with Stuart Rankin and Ortho Flint in 2007) added by _Andrey Zabolotskiy_, Jun 08 2022