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

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =3a(5) =4a(6) =5a(7) =7a(8) =10a(9) =13a(10) =18a(11) =24a(12) =33a(13) =45a(14) =62a(15) =85a(16) =116a(17) =158a(18) =216a(19) =296a(20) =404a(21) =551a(22) =753a(23) =1029a(24) =1406a(25) =1920a(26) =2623a(27) =3583a(28) =4895a(29) =6687