a(n) = Lucas(n+2) - 3.

Terms

a(0) =1a(1) =4a(2) =8a(3) =15a(4) =26a(5) =44a(6) =73a(7) =120a(8) =196a(9) =319a(10) =518a(11) =840a(12) =1361a(13) =2204a(14) =3568a(15) =5775a(16) =9346a(17) =15124a(18) =24473a(19) =39600a(20) =64076a(21) =103679a(22) =167758a(23) =271440a(24) =439201a(25) =710644a(26) =1149848a(27) =1860495a(28) =3010346a(29) =4870844