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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =6a(6) =16a(7) =36a(8) =72a(9) =136a(10) =256a(11) =496a(12) =992a(13) =2016a(14) =4096a(15) =8256a(16) =16513a(17) =32913a(18) =65689a(19) =131785a(20) =266482a(21) =544230a(22) =1124344a(23) =2352188a(24) =4984968a(25) =10699656a(26) =23244976a(27) =51072256a(28) =113370112a(29) =253930816