a(n) = Sum_{k=0..n} (-1)^k * binomial(n+2*k+5,n-k) * Fibonacci(k+1).

Terms

a(0) =1a(1) =5a(2) =14a(3) =32a(4) =77a(5) =207a(6) =565a(7) =1488a(8) =3844a(9) =9989a(10) =26212a(11) =68880a(12) =180428a(13) =471794a(14) =1234344a(15) =3232225a(16) =8464915a(17) =22162520a(18) =58015880a(19) =151878355a(20) =397630131a(21) =1041040695a(22) =2725491954a(23) =7135360142a(24) =18680513447a(25) =48906301592a(26) =128038709140a(27) =335209825828a(28) =877589936304