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

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =12a(7) =28a(8) =64a(9) =137a(10) =282a(11) =583a(12) =1244a(13) =2733a(14) =6062a(15) =13343a(16) =28944a(17) =61969a(18) =131602a(19) =278483a(20) =588564a(21) =1242646a(22) =2618924a(23) =5505556a(24) =11542528a(25) =24142217a(26) =50409898a(27) =105154719a(28) =219278860a(29) =457362189