%I #12 Jul 07 2020 06:43:21

%S 1,0,2,2,3,4,7,10,16,24,39,60,97,152,246,390,631,1008,1631,2618,4236,

%T 6820,11035,17800,28801,46512,75258,121626,196795,318188,514839,

%U 832650,1347256,2179296,3526175,5704484,9230049,14932936,24161998,39092350,63252751,102340920

%N a(n) = Fibonacci(n-1) + Fibonacci(floor(n/2)).

%C For n>=2, a(n) is the number of oriented rational links with crossing number n and deficiency 0.

%H Yuanan Diao, Michael Finney, and Dawn Ray, <a href="https://arxiv.org/abs/2007.02819">The number of oriented rational links with a given deficiency number</a>, arXiv:2007.02819 [math.GT], 2020. See Remark 5 p. 16.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,0,-1,-1).

%F G.f.: -(3*x^4-x^3+x-1)/((x^2+x-1)*(x^4+x^2-1)). - _Alois P. Heinz_, Jul 07 2020

%o (PARI) a(n) = fibonacci(n-1) + fibonacci(n\2);

%Y Cf. A000045 (Fibonacci numbers).

%K nonn,easy

%O 0,3

%A _Michel Marcus_, Jul 07 2020