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

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =6a(5) =10a(6) =15a(7) =22a(8) =34a(9) =57a(10) =101a(11) =181a(12) =319a(13) =549a(14) =928a(15) =1557a(16) =2617a(17) =4427a(18) =7536a(19) =12872a(20) =21992a(21) =37513a(22) =63862a(23) =108575a(24) =184524a(25) =313701a(26) =533619a(27) =908140a(28) =1545839a(29) =2631240