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

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =7a(5) =18a(6) =49a(7) =120a(8) =264a(9) =544a(10) =1100a(11) =2256a(12) =4736a(13) =10080a(14) =21456a(15) =45312a(16) =94850a(17) =197412a(18) =410134a(19) =852968a(20) =1778382a(21) =3719364a(22) =7806338a(23) =16451280a(24) =34835184a(25) =74164800a(26) =158854536a(27) =342478432a(28) =743432288a(29) =1625079936