a(n) = Sum_{k=0..n} binomial(n+k,2k)*Fibonacci(2k+1).

Terms

a(0) =1a(1) =3a(2) =12a(3) =51a(4) =221a(5) =965a(6) =4227a(7) =18540a(8) =81363a(9) =357145a(10) =1567849a(11) =6883059a(12) =30218028a(13) =132664227a(14) =582428789a(15) =2557009709a(16) =11225925267a(17) =49284687948a(18) =216372426339a(19) =949930508209