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

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =14a(5) =31a(6) =66a(7) =141a(8) =304a(9) =656a(10) =1413a(11) =3042a(12) =6551a(13) =14110a(14) =30390a(15) =65451a(16) =140962a(17) =303593a(18) =653856a(19) =1408224a(20) =3032921a(21) =6532066a(22) =14068251a(23) =30299094a(24) =65255806a(25) =140542823a(26) =302690082a(27) =651910101a(28) =1404032720a(29) =3023895280