a(n) = T(n, n+3), T given by A027052.

Terms

a(0) =1a(1) =8a(2) =23a(3) =52a(4) =107a(5) =210a(6) =401a(7) =754a(8) =1405a(9) =2604a(10) =4811a(11) =8872a(12) =16343a(13) =30086a(14) =55365a(15) =101862a(16) =187385a(17) =344688a(18) =634015a(19) =1166172a(20) =2144963a(21) =3945242a(22) =7256473a(23) =13346778a(24) =24548597a(25) =45151956a(26) =83047443a(27) =152748112a(28) =280947631a(29) =516743310