a(n) = a(n-1) + floor(a(n-2)/3) with a(0)=2, a(1)=3.

Terms

a(0) =2a(1) =3a(2) =3a(3) =4a(4) =5a(5) =6a(6) =7a(7) =9a(8) =11a(9) =14a(10) =17a(11) =21a(12) =26a(13) =33a(14) =41a(15) =52a(16) =65a(17) =82a(18) =103a(19) =130a(20) =164a(21) =207a(22) =261a(23) =330a(24) =417a(25) =527a(26) =666a(27) =841a(28) =1063a(29) =1343