a(n) = (10*4^n - 3*(-4)^n - 22)/30.

Terms

a(0) =1a(1) =3a(2) =27a(3) =59a(4) =443a(5) =955a(6) =7099a(7) =15291a(8) =113595a(9) =244667a(10) =1817531a(11) =3914683a(12) =29080507a(13) =62634939a(14) =465288123a(15) =1002159035a(16) =7444609979a(17) =16034544571a(18) =119113759675a(19) =256552713147