a(n) = 2^n*(3*n^2 + 13*n + 8)/8.

Terms

a(0) =1a(1) =6a(2) =23a(3) =74a(4) =216a(5) =592a(6) =1552a(7) =3936a(8) =9728a(9) =23552a(10) =56064a(11) =131584a(12) =305152a(13) =700416a(14) =1593344a(15) =3596288a(16) =8060928a(17) =17956864a(18) =39780352a(19) =87687168a(20) =192413696a(21) =420478976a(22) =915406848a(23) =1986002944a(24) =4294967296a(25) =9261023232a(26) =19914555392a(27) =42714791936