a(n) = ((3*n+1)*2^n - (-1)^n)/9.

Terms

a(0) =0a(1) =1a(2) =3a(3) =9a(4) =23a(5) =57a(6) =135a(7) =313a(8) =711a(9) =1593a(10) =3527a(11) =7737a(12) =16839a(13) =36409a(14) =78279a(15) =167481a(16) =356807a(17) =757305a(18) =1601991a(19) =3378745a(20) =7107015a(21) =14913081a(22) =31224263a(23) =65244729a(24) =136081863a(25) =283348537a(26) =589066695a(27) =1222872633a(28) =2535223751a(29) =5249404473