a(1) = a(2) = a(3) = 1; for n > 3, a(n) = ceiling((a(n-1) + a(n-2) + a(n-3))/2).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =3a(6) =4a(7) =5a(8) =6a(9) =8a(10) =10a(11) =12a(12) =15a(13) =19a(14) =23a(15) =29a(16) =36a(17) =44a(18) =55a(19) =68a(20) =84a(21) =104a(22) =128a(23) =158a(24) =195a(25) =241a(26) =297a(27) =367a(28) =453a(29) =559