a(n) = 2*a(n-1) + a(n-2) - a(n-3), where a(0) = 2, a(1) = 3, a(2) = 6.

Terms

a(0) =2a(1) =3a(2) =6a(3) =13a(4) =29a(5) =65a(6) =146a(7) =328a(8) =737a(9) =1656a(10) =3721a(11) =8361a(12) =18787a(13) =42214a(14) =94854a(15) =213135a(16) =478910a(17) =1076101a(18) =2417977a(19) =5433145a(20) =12208166a(21) =27431500a(22) =61638021a(23) =138499376a(24) =311205273a(25) =699271901a(26) =1571249699a(27) =3530566026a(28) =7933109850a(29) =17825536027