a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-3*k-1,k) * a(k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =3a(7) =4a(8) =5a(9) =7a(10) =10a(11) =14a(12) =19a(13) =26a(14) =36a(15) =50a(16) =69a(17) =95a(18) =131a(19) =181a(20) =250a(21) =346a(22) =482a(23) =678a(24) =963a(25) =1380a(26) =1994a(27) =2903a(28) =4252a(29) =6254