a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k+1).

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =4a(5) =5a(6) =7a(7) =12a(8) =23a(9) =44a(10) =80a(11) =138a(12) =230a(13) =379a(14) =629a(15) =1060a(16) =1810a(17) =3109a(18) =5336a(19) =9120a(20) =15521a(21) =26349a(22) =44713a(23) =75949a(24) =129177a(25) =219918a(26) =374521a(27) =637699a(28) =1085401a(29) =1846804