n*3^(n-1)+A081567(n).

Terms

a(0) =1a(1) =4a(2) =16a(3) =62a(4) =233a(5) =855a(6) =3083a(7) =10978a(8) =38746a(9) =135924a(10) =474955a(11) =1655789a(12) =5766389a(13) =20080608a(14) =69976772a(15) =244166410a(16) =853410637a(17) =2988825507a(18) =10490538559a(19) =36905911166a(20) =130139760590a(21) =459970519296