a(n) = Sum_{k=0..n} (2^k + 2) * (2^k + 3) / 2.

Terms

a(0) =6a(1) =16a(2) =37a(3) =92a(4) =263a(5) =858a(6) =3069a(7) =11584a(8) =44995a(9) =177350a(10) =704201a(11) =2806476a(12) =11205327a(13) =44780242a(14) =179038933a(15) =715991768a(16) =2863639259a(17) =11453901534a(18) =45814295265a(19) =183254559460a(20) =733012994791