a(n) = a(n-1) + a(n-2) + a([2n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.

Terms

a(0) =1a(1) =2a(2) =3a(3) =8a(4) =14a(5) =30a(6) =58a(7) =102a(8) =190a(9) =350a(10) =598a(11) =1050a(12) =1838a(13) =3078a(14) =5266a(15) =8942a(16) =14806a(17) =24798a(18) =41442a(19) =68078a(20) =112598a(21) =185942a(22) =303806a(23) =498690a(24) =817302a(25) =1330798a(26) =2172898a(27) =3545138a(28) =5759478a(29) =9372694