a(n) = Sum_{k=0..floor(n/3)} 2^k * Stirling2(n,3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =12a(5) =50a(6) =184a(7) =686a(8) =2996a(9) =16642a(10) =110328a(11) =784190a(12) =5645876a(13) =40685762a(14) =296458344a(15) =2226254766a(16) =17564381332a(17) =147289101090