a(n) = Sum_{k=0..n} ceiling(phi^k), where phi is the golden ratio (A001622).

Terms

a(0) =1a(1) =3a(2) =6a(3) =11a(4) =18a(5) =30a(6) =48a(7) =78a(8) =125a(9) =202a(10) =325a(11) =525a(12) =847a(13) =1369a(14) =2212a(15) =3577a(16) =5784a(17) =9356a(18) =15134a(19) =24484a(20) =39611a(21) =64088a(22) =103691a(23) =167771a(24) =271453a(25) =439215a(26) =710658a(27) =1149863a(28) =1860510a(29) =3010362