Floor((x^n - (1-x)^n)/2 +.5) where x = (sqrt(4)+1)/2 = 3/2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =9a(7) =13a(8) =19a(9) =29a(10) =43a(11) =65a(12) =97a(13) =146a(14) =219a(15) =328a(16) =493a(17) =739a(18) =1108a(19) =1663a(20) =2494a(21) =3741a(22) =5611a(23) =8417a(24) =12626a(25) =18938a(26) =28408a(27) =42611a(28) =63917a(29) =95876