a(n) = Lucas(n+1) + (3*(-1)^n - 1)/2.

Terms

a(0) =2a(1) =1a(2) =5a(3) =5a(4) =12a(5) =16a(6) =30a(7) =45a(8) =77a(9) =121a(10) =200a(11) =320a(12) =522a(13) =841a(14) =1365a(15) =2205a(16) =3572a(17) =5776a(18) =9350a(19) =15125a(20) =24477a(21) =39601a(22) =64080a(23) =103680a(24) =167762a(25) =271441a(26) =439205a(27) =710645a(28) =1149852a(29) =1860496