a(n) = floor((x^n - (1-x)^n) / (2x-1) +.5) where x = (sqrt(6)+1)/2 (and hence 2x-1 = sqrt(6)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =6a(5) =11a(6) =19a(7) =32a(8) =55a(9) =95a(10) =164a(11) =283a(12) =488a(13) =842a(14) =1451a(15) =2503a(16) =4318a(17) =7447a(18) =12844a(19) =22152a(20) =38207a(21) =65898a(22) =113657a(23) =196029a(24) =338101a(25) =583137a(26) =1005763a(27) =1734685a(28) =2991888a(29) =5160244