a(n) = Lucas(4*n+2)-2 = Lucas(2*n+1)^2.

Terms

a(0) =1a(1) =16a(2) =121a(3) =841a(4) =5776a(5) =39601a(6) =271441a(7) =1860496a(8) =12752041a(9) =87403801a(10) =599074576a(11) =4106118241a(12) =28143753121a(13) =192900153616