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

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =13a(5) =23a(6) =43a(7) =73a(8) =129a(9) =215a(10) =367a(11) =605a(12) =1015a(13) =1663a(14) =2751a(15) =4487a(16) =7367a(17) =11983a(18) =19565a(19) =31763a(20) =51695a(21) =83825a(22) =136125a(23) =220555a(24) =357695a(25) =579265a(26) =938623a(27) =1519551a(28) =2460925a(29) =3983227