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A172293
a(n) = number of prime knots up to nine crossings with determinant 2n+1 and signature 0.
7
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.
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
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