a(n) = Sum_{k=0..n} (2^k + 1) * (2^k + 2) / 2.

Terms

a(0) =3a(1) =9a(2) =24a(3) =69a(4) =222a(5) =783a(6) =2928a(7) =11313a(8) =44466a(9) =176307a(10) =702132a(11) =2802357a(12) =11197110a(13) =44763831a(14) =179006136a(15) =715926201a(16) =2863508154a(17) =11453639355a(18) =45813770940a(19) =183253510845a(20) =733010897598