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

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%I A172293 #17 Apr 30 2024 01:56:14
%S A172293 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
%N A172293 a(n) = number of prime knots up to nine crossings with determinant 2n+1 and signature 0.
%D A172293 Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004. See p. 146, Fig. 6.6.
%e A172293 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.
%e A172293 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.
%e A172293 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.
%Y A172293 Cf. A002863.
%Y A172293 First column of A172184.
%K A172293 nonn,fini,full
%O A172293 0,5
%A A172293 _Jonathan Vos Post_, Nov 20 2010
%E A172293 Partially edited by _N. J. A. Sloane_, Jun 10 2019
%E A172293 Edited by _Andrey Zabolotskiy_, Apr 29 2024