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A172184 Table read by antidiagonals: T(n,k) = number of prime knots with determinant 2n+1 and signature 2k. 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,11

REFERENCES

Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 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 determinant 2*0+1=1 and s=0 is 0_1, the unknot.

T(1,1) = 1 because the only prime knot 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 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.

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

STATUS

approved

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Last modified September 23 11:36 EDT 2021. Contains 347612 sequences. (Running on oeis4.)