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

Author

Jonathan Vos Post, Nov 20 2010

Keywords

• nonn
• fini
• full

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.

Examples

			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.
		

References

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

Crossrefs

Cf. A002863, A172184, A172293.

Extensions

Edited by Andrey Zabolotskiy, Apr 29 2024