a(n) = floor(x^n) where x = 1 + sqrt(5)/2 = A176055.

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =20a(5) =42a(6) =90a(7) =191a(8) =405a(9) =857a(10) =1816a(11) =3848a(12) =8150a(13) =17263a(14) =36564a(15) =77445a(16) =164031a(17) =347423a(18) =735855a(19) =1558567a(20) =3301098a(21) =6991839a(22) =14808952a(23) =31365865a(24) =66433969a(25) =140709405a(26) =298027302a(27) =631231956a(28) =1336970739a(29) =2831749467