Binomial transform of 1,0,1,0,1,1,1,...

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =17a(6) =38a(7) =86a(8) =192a(9) =419a(10) =894a(11) =1872a(12) =3864a(13) =7893a(14) =16006a(15) =32298a(16) =64960a(17) =130375a(18) =261310a(19) =523300a(20) =1047416a(21) =2095801a(22) =4192742a(23) =8386814a(24) =16775168a(25) =33552107a(26) =67106238a(27) =134214776a(28) =268432152a(29) =536867229