A049344 - OEIS

A049344

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

0, 1, 1, 2, 3, 8, 14, 39, 96, 297, 915, 3308, 12417, 51347, 222595, 1016975, 4799520, 23301779, 115405815, 581071711, 2963793396, 15283327150, 79544488072, 417377448058

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..24.

S. R. Finch, Knots, links and tangles [dead link]

S. R. Finch, Knots, links and tangles, Aug 08 2003. [Cached copy, with permission of the author]

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 626.

Bruce Fontaine, Knots/Links

Stavros Garoufalidis and Thao Vuong, Alternating knots, planar graphs, and q-series, The Ramanujan Journal 36.3 (2015): 501-527; arXiv:1304.1071 [math.GT], 2013. See (28).

CROSSREFS

Cf. A002864, A086771. Row sums of A059739.

Sequence in context: A201361 A129700 A197466 * A080877 A007165 A107321

Adjacent sequences: A049341 A049342 A049343 * A049345 A049346 A049347

KEYWORD

nonn,nice,hard,more

AUTHOR

N. J. A. Sloane, Feb 10 2001

EXTENSIONS

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

STATUS

approved