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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =13a(6) =33a(7) =91a(8) =223a(9) =597a(10) =1753a(11) =4963a(12) =14391a(13) =44413a(14) =137137a(15) =427083a(16) =1382383a(17) =4534981a(18) =14981673a(19) =50719507a(20) =174494983a(21) =605276973a(22) =2135204161a(23) =7647369403a(24) =27643067007a(25) =101211363253a(26) =375548195833