a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3) if n>=3, otherwise a(n) = n.

Terms

a(0) =0a(1) =1a(2) =2a(3) =8a(4) =29a(5) =105a(6) =381a(7) =1382a(8) =5013a(9) =18184a(10) =65960a(11) =239261a(12) =867887a(13) =3148143a(14) =11419464a(15) =41422565a(16) =150254766a(17) =545028892a(18) =1977018773a(19) =7171368869a(20) =26013173045a(21) =94359275646a(22) =342275541897