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Number of prime knots up to nine crossings with determinant 2n+1 and signature 4.
5

%I #13 Apr 30 2024 01:56:08

%S 0,0,1,0,0,0,2,0,2,0,2,0,1,0,1,0,3,0,2,0,2,0,1,0,0,0,0,0,1

%N Number of prime knots up to nine crossings with determinant 2n+1 and signature 4.

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

%D Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004.

%e a(2) = 1 because the only prime knot with no more than 9 crossings with determinant 2*2+1=5 and s=4 is 5_1, the Solomon's seal knot.

%e a(6) = 2 because the only prime knots with no more than 9 crossings with determinant 2*6+1=13 and s=4 are 7_3 and 9_43.

%Y Cf. A002863, A172184, A172293, A172441.

%K nonn,fini,full

%O 0,7

%A _Jonathan Vos Post_, Nov 20 2010

%E Edited by _Andrey Zabolotskiy_, Apr 29 2024