a(n) = Sum_{k=0..n} C(n-k, floor(k/2)).

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =5a(5) =7a(6) =10a(7) =15a(8) =22a(9) =32a(10) =47a(11) =69a(12) =101a(13) =148a(14) =217a(15) =318a(16) =466a(17) =683a(18) =1001a(19) =1467a(20) =2150a(21) =3151a(22) =4618a(23) =6768a(24) =9919a(25) =14537a(26) =21305a(27) =31224a(28) =45761a(29) =67066