A172293 a(n) = number of prime knots up to nine crossings with determinant 2n+1 and signature 0.

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

Offset: 0

Author

Jonathan Vos Post, Nov 20 2010

Keywords

• nonn
• fini
• full

Examples

			a(0) = 1 because the only prime knot with no more than 9 crossings with determinant 2*0+1=1 and s=0 is 0_1, the unknot.
a(2) = 1 because the only prime knot with no more than 9 crossings with determinant 2*2+1=5 and s=0 is 4_1, the figure-8 knot.
a(4) = 3 because the three prime knots with no more than 9 crossings with determinant 2*4+1=9 and s=0 are 6_1, 8_20, and 9_46.
		

References

• Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004. See p. 146, Fig. 6.6.

Crossrefs

Cf. A002863.

First column of A172184.

Extensions

Partially edited by N. J. A. Sloane, Jun 10 2019

Edited by Andrey Zabolotskiy, Apr 29 2024