Number of binary sequences of length n containing exactly one subsequence 001.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =4a(5) =12a(6) =30a(7) =68a(8) =144a(9) =291a(10) =568a(11) =1080a(12) =2012a(13) =3688a(14) =6672a(15) =11941a(16) =21180a(17) =37284a(18) =65210a(19) =113420a(20) =196320a(21) =338375a(22) =581040a(23) =994416a(24) =1696824a(25) =2887632a(26) =4902240a(27) =8304073a(28) =14038324a(29) =23688636