a(n) = F(n+1)^2, if n>=0 is even (F=A000045) and a(n) = (L(2n+2)+8)/5, if n is odd (L=A000204).

Terms

a(0) =1a(1) =3a(2) =4a(3) =11a(4) =25a(5) =66a(6) =169a(7) =443a(8) =1156a(9) =3027a(10) =7921a(11) =20738a(12) =54289a(13) =142131a(14) =372100a(15) =974171a(16) =2550409a(17) =6677058a(18) =17480761a(19) =45765227a(20) =119814916a(21) =313679523a(22) =821223649a(23) =2149991426a(24) =5628750625a(25) =14736260451a(26) =38580030724a(27) =101003831723a(28) =264431464441a(29) =692290561602