a(n) = floor((3*4^n - 2*3^n)/5).

Terms

a(0) =0a(1) =1a(2) =6a(3) =27a(4) =121a(5) =517a(6) =2166a(7) =8955a(8) =36697a(9) =149413a(10) =605526a(11) =2445723a(12) =9853753a(13) =39627589a(14) =159148086a(15) =638505531a(16) =2559761689a(17) =10256265445a(18) =41076717846a(19) =164461839579a(20) =658312262905