a(n) = 10*a(n-3) - a(n-6) + 4 for n>5, a(0)=2, a(1)=3, a(2)=5, a(3)=12, a(4)=29, a(5)=51.

Terms

a(0) =2a(1) =3a(2) =5a(3) =12a(4) =29a(5) =51a(6) =122a(7) =291a(8) =509a(9) =1212a(10) =2885a(11) =5043a(12) =12002a(13) =28563a(14) =49925a(15) =118812a(16) =282749a(17) =494211a(18) =1176122a(19) =2798931a(20) =4892189a(21) =11642412a(22) =27706565a(23) =48427683a(24) =115248002a(25) =274266723a(26) =479384645a(27) =1140837612a(28) =2714960669a(29) =4745418771