a(n) = Lucas(5*n+2).

Terms

a(0) =3a(1) =29a(2) =322a(3) =3571a(4) =39603a(5) =439204a(6) =4870847a(7) =54018521a(8) =599074578a(9) =6643838879a(10) =73681302247a(11) =817138163596