Number of binary strings of length n with equal numbers of 0000 and 1001 substrings.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =25a(6) =44a(7) =77a(8) =137a(9) =245a(10) =442a(11) =802a(12) =1467a(13) =2701a(14) =5007a(15) =9337a(16) =17514a(17) =33025a(18) =62580a(19) =119107a(20) =227609a(21) =436522a(22) =839915a(23) =1620774a(24) =3135715a(25) =6080701a(26) =11815887a(27) =23002577a(28) =44853764a(29) =87590551