Number of binary strings of length n with equal numbers of 0001 and 1001 substrings.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =24a(6) =40a(7) =67a(8) =114a(9) =200a(10) =364a(11) =684a(12) =1316a(13) =2565a(14) =5025a(15) =9843a(16) =19232a(17) =37464a(18) =72808a(19) =141327a(20) =274332a(21) =533044a(22) =1037436a(23) =2022982a(24) =3952284a(25) =7734625a(26) =15157799a(27) =29737631a(28) =58389819a(29) =114721663