A172444 Number of prime knots up to nine crossings with determinant 2n+1 and signature 4.

0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 3, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1

Offset

0,7

Comments

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

References

Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004.

Links

Table of n, a(n) for n=0..28.

Example

a(2) = 1 because the only prime knot with no more than 9 crossings with determinant 2*2+1=5 and s=4 is 5_1, the Solomon's seal knot.
a(6) = 2 because the only prime knots with no more than 9 crossings with determinant 2*6+1=13 and s=4 are 7_3 and 9_43.

Crossrefs

Cf. A002863, A172184, A172293, A172441.

Sequence in context: A174479 A134269 A335622 * A277146 A353460 A026611

Adjacent sequences: A172441 A172442 A172443 * A172445 A172446 A172447

Keyword

nonn,fini,full

Author

Jonathan Vos Post, Nov 20 2010

Extensions

Edited by Andrey Zabolotskiy, Apr 29 2024

Status

approved