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

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =12a(5) =22a(6) =37a(7) =66a(8) =110a(9) =188a(10) =310a(11) =520a(12) =852a(13) =1409a(14) =2298a(15) =3773a(16) =6137a(17) =10020a(18) =16267a(19) =26475a(20) =42930a(21) =69715a(22) =112955a(23) =183190a(24) =296665a(25) =480707a(26) =778224a(27) =1260340a(28) =2039973a(29) =3302611