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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
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
Sequence in context: A232006 A202820 A113081 * A109865 A206713 A096874
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 March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)