a(n) = ((9*n^2 + 33*n + 26)*2^n + (-1)^n)/27.

Terms

a(0) =1a(1) =5a(2) =19a(3) =61a(4) =179a(5) =493a(6) =1299a(7) =3309a(8) =8211a(9) =19949a(10) =47635a(11) =112109a(12) =260627a(13) =599533a(14) =1366547a(15) =3089901a(16) =6937107a(17) =15476205a(18) =34331155a(19) =75769325a(20) =166451731a(21) =364127725a(22) =793500179a(23) =1723082221a(24) =3729512979a(25) =8048092653a(26) =17319057939