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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =6a(7) =16a(8) =36a(9) =72a(10) =136a(11) =256a(12) =496a(13) =992a(14) =2016a(15) =4096a(16) =8256a(17) =16512a(18) =32896a(19) =65536a(20) =130816a(21) =261633a(22) =523797a(23) =1048807a(24) =2099947a(25) =4206983a(26) =8443911a(27) =17009071a(28) =34452991a(29) =70311167