Partitioning integers to avoid arithmetic progressions of length 3.

Terms

a(0) =0a(1) =1a(2) =2a(3) =4a(4) =7a(5) =11a(6) =17a(7) =26a(8) =40a(9) =61a(10) =92a(11) =139a(12) =209a(13) =314a(14) =472a(15) =709a(16) =1064a(17) =1597a(18) =2396a(19) =3595a(20) =5393a(21) =8090a(22) =12136a(23) =18205a(24) =27308a(25) =40963a(26) =61445a(27) =92168a(28) =138253a(29) =207380