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A329908
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Number of oriented rational links with crossing number n.
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4
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2, 2, 5, 6, 15, 24, 51, 90, 187, 352, 715, 1386, 2795, 5504, 11051, 21930, 43947, 87552, 175275, 349866, 700075, 1398784, 2798251, 5593770, 11188907, 22372352, 44747435, 89483946, 178973355, 357924864, 715860651, 1431677610, 2863377067, 5726666752, 11453377195
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) = (2^(n-1)+1)/3 + 2^(n/2-1) if n is even; (2^(n-1)+2^((n-1)/2)-2)/3 if n is odd and n == 1 mod 4; (2^(n-1)+2^((n-1)/2))/3) if n is odd and n == 3 mod 4.
G.f.: x^2*(2 - 3*x^2 - 3*x^3 - 4*x^4)/(1 - x - 3*x^2 + x^3 + 2*x^5 + 4*x^6). - Jinyuan Wang, Jul 08 2020
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PROG
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(PARI) a(n) = if (n%2, if ((n%4)==1, (2^(n-1)+2^((n-1)/2)-2)/3, (2^(n-1)+2^((n-1)/2))/3), (2^(n-1)+1)/3 + 2^(n/2-1));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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