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

Terms

a(0) =1a(1) =2a(2) =5a(3) =14a(4) =39a(5) =106a(6) =283a(7) =748a(8) =1967a(9) =5160a(10) =13521a(11) =35412a(12) =92725a(13) =242774a(14) =635609a(15) =1664066a(16) =4356603a(17) =11405758a(18) =29860687a(19) =78176320a(20) =204668291a(21) =535828572a(22) =1402817445a(23) =3672623784a(24) =9615053929a(25) =25172538026a(26) =65902560173a(27) =172535142518