a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3), with a(0) = 2, a(1) = 5, a(2) = 12.

Terms

a(0) =2a(1) =5a(2) =12a(3) =28a(4) =65a(5) =150a(6) =346a(7) =797a(8) =1836a(9) =4228a(10) =9737a(11) =22422a(12) =51634a(13) =118901a(14) =273804a(15) =630508a(16) =1451921a(17) =3343446a(18) =7699210a(19) =17729549a(20) =40827180a(21) =94015828a(22) =216497369a(23) =498544854a(24) =1148036962a(25) =2643671525a(26) =6087782412a(27) =14018796988a(28) =32282144225a(29) =74338535190