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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =11a(6) =21a(7) =37a(8) =69a(9) =127a(10) =217a(11) =381a(12) =667a(13) =1117a(14) =1911a(15) =3245a(16) =5373a(17) =8999a(18) =15039a(19) =24705a(20) =40861a(21) =67477a(22) =110249a(23) =180971a(24) =296593a(25) =482937a(26) =788529a(27) =1286505a(28) =2090073a(29) =3401283