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

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =12a(5) =21a(6) =36a(7) =60a(8) =99a(9) =166a(10) =272a(11) =445a(12) =729a(13) =1186a(14) =1927a(15) =3134a(16) =5082a(17) =8237a(18) =13355a(19) =21628a(20) =35019a(21) =56707a(22) =91786a(23) =148553a(24) =240438a(25) =389090a(26) =629627a(27) =1018883a(28) =1648676a(29) =2667725