a(n)=a(n-1)+a(n-2)-d, where d=a(n/3) if 3 divides n, else d=0; 2 initial terms.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =7a(7) =11a(8) =17a(9) =28a(10) =45a(11) =71a(12) =116a(13) =187a(14) =300a(15) =487a(16) =787a(17) =1270a(18) =2057a(19) =3327a(20) =5377a(21) =8704a(22) =14081a(23) =22774a(24) =36855a(25) =59629a(26) =96467a(27) =156096a(28) =252563a(29) =408631