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

0,5

References

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

Links

Table of n, a(n) for n=0..34.

Example

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.

Crossrefs

Cf. A002863.

First column of A172184.

Sequence in context: A166243 A118514 A190544 * A353461 A161970 A230446

Adjacent sequences: A172290 A172291 A172292 * A172294 A172295 A172296

Keyword

nonn,fini,full

Author

Jonathan Vos Post, Nov 20 2010

Extensions

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

Edited by Andrey Zabolotskiy, Apr 29 2024

Status

approved