a(n) = (3^n + 2*n*3^(n-1) - 1)/4.

Terms

a(0) =0a(1) =1a(2) =5a(3) =20a(4) =74a(5) =263a(6) =911a(7) =3098a(8) =10388a(9) =34445a(10) =113177a(11) =369056a(12) =1195742a(13) =3852947a(14) =12356003a(15) =39459494a(16) =125552936a(17) =398182169a(18) =1259116589a(19) =3971060012a(20) =12494310770a(21) =39226324511a(22) =122909150135a(23) =384417980210