Number of subsets of [n] avoiding 3-term arithmetic progressions and containing n if n>0.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =17a(7) =25a(8) =41a(9) =63a(10) =109a(11) =165a(12) =262a(13) =412a(14) =643a(15) =932a(16) =1459a(17) =2163a(18) =3212a(19) =4601a(20) =6817a(21) =9904a(22) =14741a(23) =20906a(24) =30352a(25) =43993a(26) =63540a(27) =89442a(28) =132037a(29) =187587