a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), 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) =19a(7) =35a(8) =59a(9) =105a(10) =175a(11) =299a(12) =493a(13) =827a(14) =1355a(15) =2241a(16) =3655a(17) =6001a(18) =9761a(19) =15937a(20) =25873a(21) =42109a(22) =68281a(23) =110883a(24) =179657a(25) =291367a(26) =471851a(27) =764573a(28) =1237779a(29) =2004593