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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =2a(7) =4a(8) =8a(9) =17a(10) =38a(11) =89a(12) =219a(13) =567a(14) =1543a(15) =4400a(16) =13094a(17) =40507a(18) =129874a(19) =430731a(20) =1476030a(21) =5222544a(22) =19066758a(23) =71764369a(24) =278166767a(25) =1108986222a(26) =4541765652a(27) =19085377108a(28) =82211094414a(29) =362717859475