a(n) = floor((x^n-(1-x)^n)/sqrt(7)+1/2) where x = (sqrt(7)+1)/2.

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =8a(5) =14a(6) =25a(7) =46a(8) =84a(9) =153a(10) =279a(11) =509a(12) =927a(13) =1691a(14) =3082a(15) =5618a(16) =10241a(17) =18667a(18) =34028a(19) =62029a(20) =113070a(21) =206113a(22) =375719a(23) =684889a(24) =1248467a(25) =2275800a(26) =4148501a(27) =7562201a(28) =13784953a(29) =25128255