a(n) = Sum_{k=0..floor(n/6)} binomial(n-3k,3k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =2a(7) =5a(8) =11a(9) =21a(10) =36a(11) =57a(12) =86a(13) =128a(14) =194a(15) =305a(16) =497a(17) =827a(18) =1381a(19) =2287a(20) =3739a(21) =6042a(22) =9693a(23) =15519a(24) =24901a(25) =40126a(26) =64933a(27) =105364a(28) =171112a(29) =277696