a(n) = (6^n + 4^n + 3*2^n)/8.

Terms

a(0) =2a(1) =8a(2) =38a(3) =200a(4) =1112a(5) =6368a(6) =37088a(7) =218240a(8) =1292672a(9) =7689728a(10) =45874688a(11) =274196480a(12) =1640978432a(13) =9829081088a(14) =58907353088a(15) =353175633920