Half-indexed Lucas numbers a(n)=round(sqrt((1+sqrt(5))/2)^n) a(2n)=L(n)=A000032, so a(n)=L(n/2).

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =3a(5) =4a(6) =5a(7) =7a(8) =9a(9) =11a(10) =14a(11) =18a(12) =23a(13) =29a(14) =37a(15) =47a(16) =60a(17) =76a(18) =97a(19) =123a(20) =156a(21) =199a(22) =253a(23) =322a(24) =410a(25) =521a(26) =663a(27) =843a(28) =1072a(29) =1364