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

Terms

a(0) =0a(1) =1a(2) =3a(3) =9a(4) =28a(5) =90a(6) =297a(7) =1001a(8) =3431a(9) =11917a(10) =41820a(11) =147918a(12) =526309a(13) =1881009a(14) =6744843a(15) =24244145a(16) =87300092a(17) =314765506a(18) =1135980801a(19) =4102551897a(20) =14823628015a(21) =53581222773a(22) =193724727804a(23) =700551945014