Lucas numbers (A000204) of the form n^2 + 2.

Terms

a(0) =3a(1) =11a(2) =18a(3) =123a(4) =843a(5) =5778a(6) =39603a(7) =271443a(8) =1860498a(9) =12752043a(10) =87403803a(11) =599074578a(12) =4106118243a(13) =28143753123a(14) =192900153618