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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =8a(5) =17a(6) =35a(7) =75a(8) =163a(9) =352a(10) =757a(11) =1629a(12) =3509a(13) =7559a(14) =16280a(15) =35061a(16) =75511a(17) =162631a(18) =350263a(19) =754368a(20) =1624697a(21) =3499145a(22) =7536185a(23) =16230843a(24) =34956712a(25) =75287017a(26) =162147259a(27) =349220019a(28) =752122619a(29) =1619862560