A336030 a(n) = Fibonacci(n-1) + Fibonacci(floor(n/2)).

1, 0, 2, 2, 3, 4, 7, 10, 16, 24, 39, 60, 97, 152, 246, 390, 631, 1008, 1631, 2618, 4236, 6820, 11035, 17800, 28801, 46512, 75258, 121626, 196795, 318188, 514839, 832650, 1347256, 2179296, 3526175, 5704484, 9230049, 14932936, 24161998, 39092350, 63252751, 102340920

Offset: 0

Author

Michel Marcus, Jul 07 2020

Keywords

• nonn
• easy

Comments

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

Links

• Yuanan Diao, Michael Finney, and Dawn Ray, The number of oriented rational links with a given deficiency number, arXiv:2007.02819 [math.GT], 2020. See Remark 5 p. 16.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-1,0,-1,-1).

Crossrefs

Cf. A000045 (Fibonacci numbers).

Programs

PARI

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

Formula

G.f.: -(3*x^4-x^3+x-1)/((x^2+x-1)*(x^4+x^2-1)). - Alois P. Heinz, Jul 07 2020