a(n) = Sum_{k=0..floor(n/4)} Stirling2(n - 3*k,k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =1a(6) =1a(7) =1a(8) =2a(9) =4a(10) =8a(11) =16a(12) =33a(13) =70a(14) =153a(15) =346a(16) =814a(17) =2000a(18) =5138a(19) =13776a(20) =38395a(21) =110695a(22) =328638a(23) =1001306a(24) =3124626a(25) =9978906a(26) =32620854a(27) =109225582a(28) =374875483a(29) =1319392590