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

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =7a(5) =16a(6) =31a(7) =55a(8) =103a(9) =193a(10) =331a(11) =583a(12) =1024a(13) =1717a(14) =2941a(15) =5005a(16) =8293a(17) =13897a(18) =23245a(19) =38197a(20) =63190a(21) =104383a(22) =170569a(23) =280012a(24) =458977a(25) =747385a(26) =1220362a(27) =1991185a(28) =3234985a(29) =5264560