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

Terms

a(0) =2a(1) =10a(2) =17a(3) =50a(4) =122a(5) =325a(6) =842a(7) =2210a(8) =5777a(9) =15130a(10) =39602a(11) =103685a(12) =271442a(13) =710650a(14) =1860497a(15) =4870850a(16) =12752042a(17) =33385285a(18) =87403802a(19) =228826130a(20) =599074577a(21) =1568397610a(22) =4106118242a(23) =10749957125a(24) =28143753122a(25) =73681302250a(26) =192900153617a(27) =505019158610