A172184 Table read by antidiagonals: T(n,k) = number of prime knots up to nine crossings with determinant 2n+1 and signature 2k.

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

Offset

1,11

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=1..41.

Example

T(0,0) = 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.
T(1,1) = 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.
T(1,3) = 1 because the only prime knot with no more than 9 crossings with determinant 2*1+1=3 and s=6 is 8_19.
Table begins:
  =========================
  Det s=0 s=2 s=4 s=6 s=8
  =========================
   1 | 1 | 0 | 0 | 0 | 0
   3 | 0 | 1 | 0 | 1 | 0
   5 | 1 | 0 | 1 | 0 | 0
   7 | 0 | 2 | 0 | 1 | 0
   9 | 3 | 0 | 0 | 0 | 1
  11 | 0 | 2 | 0 | 0 | 0
  13 | 2 | 0 | 2 | 0 | 0
  15 | 0 | 3 | 0 | 0 | 0
  17 | 2 | 0 | 2 | 0 | 0
  =========================

Crossrefs

Cf. A002863, A172293, A172293, A172441, A172444, A172486.

Sequence in context: A232006 A202820 A113081 * A109865 A206713 A096874

Adjacent sequences: A172181 A172182 A172183 * A172185 A172186 A172187

Keyword

nonn,tabl,more

Author

Jonathan Vos Post, Nov 19 2010

Extensions

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

Name edited by Andrey Zabolotskiy, Apr 29 2024

Status

approved