A172441 Number of prime knots up to nine crossings with determinant 2n+1 and signature 2.

0, 1, 0, 2, 0, 2, 0, 3, 0, 2, 0, 4, 0, 5, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0,4

Comments

Adapted from Figure 6.6. The prime knots up to nine crossings separated by signature and determinant, p. 146, Cromwell. Second column of A172184.

References

Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004.

Links

Table of n, a(n) for n=0..37.

Example

a(1) = 1 because the only prime knot with no more than 9 crossings with determinant 2*1+1=3 and s=2 is 3_1, the left-handed trefoil.
a(3) = 2 because the only prime knots with no more than 9 crossings with determinant 2*3+1=7 and s=2 are 5_2 and 9_42.

Crossrefs

Cf. A002863, A172184, A172293.

Sequence in context: A301979 A183063 A318979 * A359495 A053399 A322996

Adjacent sequences: A172438 A172439 A172440 * A172442 A172443 A172444

Keyword

nonn,fini,full,changed

Author

Jonathan Vos Post, Nov 20 2010

Extensions

Edited by Andrey Zabolotskiy, Apr 29 2024

Status

approved