a(n) = floor(2^(n-1)) - binomial(n,3) + binomial(n,2) - n + 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =7a(5) =12a(6) =22a(7) =44a(8) =93a(9) =200a(10) =428a(11) =904a(12) =1883a(13) =3876a(14) =7906a(15) =16020a(16) =32313a(17) =64976a(18) =130392a(19) =261328a(20) =523319a(21) =1047436a(22) =2095822a(23) =4192764a(24) =8386837a(25) =16775192a(26) =33552132a(27) =67106264a(28) =134214803a(29) =268432180