a(n) = 4^n - binomial(n,2)*3^(n-2).

Terms

a(0) =1a(1) =4a(2) =15a(3) =55a(4) =202a(5) =754a(6) =2881a(7) =11281a(8) =45124a(9) =183412a(10) =753331a(11) =3111739a(12) =12879982a(13) =53291398a(14) =220074325a(15) =906337909a(16) =3721011016a(17) =15228417832a(18) =62133328423a(19) =252794939071