a(n) = Sum_{k=0..n} C(n-k,3k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =5a(6) =11a(7) =21a(8) =37a(9) =64a(10) =113a(11) =205a(12) =377a(13) =693a(14) =1266a(15) =2301a(16) =4175a(17) =7581a(18) =13785a(19) =25088a(20) =45665a(21) =83097a(22) =151169a(23) =274969a(24) =500162a(25) =909845a(26) =1655187a(27) =3011157a(28) =5477917a(29) =9965312