a(n) = Lucas(n) + (-1)^n + 1.

Terms

a(0) =1a(1) =5a(2) =4a(3) =9a(4) =11a(5) =20a(6) =29a(7) =49a(8) =76a(9) =125a(10) =199a(11) =324a(12) =521a(13) =845a(14) =1364a(15) =2209a(16) =3571a(17) =5780a(18) =9349a(19) =15129a(20) =24476a(21) =39605a(22) =64079a(23) =103684a(24) =167761a(25) =271445a(26) =439204a(27) =710649a(28) =1149851a(29) =1860500