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Number of prime knots up to nine crossings with determinant 2n+1 and signature 2.
6

%I #12 Apr 30 2024 01:56:11

%S 0,1,0,2,0,2,0,3,0,2,0,4,0,5,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,1,0,0,0,0,

%T 0,0,0,1

%N Number of prime knots up to nine crossings with determinant 2n+1 and signature 2.

%C Adapted from Figure 6.6. The prime knots up to nine crossings separated by signature and determinant, p. 146, Cromwell. Second column of A172184.

%D Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004.

%e a(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.

%e a(3) = 2 because the only prime knots with no more than 9 crossings with determinant 2*3+1=7 and s=2 are 5_2 and 9_42.

%Y Cf. A002863, A172184, A172293.

%K nonn,fini,full

%O 0,4

%A _Jonathan Vos Post_, Nov 20 2010

%E Edited by _Andrey Zabolotskiy_, Apr 29 2024