a(n) = a(n-1)+a(n-2)-Floor(a(n-3)/2)-Floor(a(n-8)/2); initial terms are 0, 1, 1, 2, 3, 5, 7, 11.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =7a(7) =11a(8) =16a(9) =24a(10) =35a(11) =50a(12) =72a(13) =103a(14) =147a(15) =209a(16) =297a(17) =421a(18) =597a(19) =845a(20) =1196a(21) =1692a(22) =2393a(23) =3383a(24) =4782a(25) =6759a(26) =9552a(27) =13498a(28) =19073a(29) =26949