a(n) = 3^(n-2)*(binomial(n,2) + 3*n + 9).

Terms

a(0) =1a(1) =4a(2) =16a(3) =63a(4) =243a(5) =918a(6) =3402a(7) =12393a(8) =44469a(9) =157464a(10) =551124a(11) =1909251a(12) =6554439a(13) =22320522a(14) =75464622a(15) =253497357a(16) =846585513a(17) =2812385772a(18) =9298091736a(19) =30606218631a(20) =100341906651a(21) =327757733694