Number of binary strings of length n which have the same number of 00 and 01 substrings.

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =6a(5) =9a(6) =15a(7) =30a(8) =54a(9) =97a(10) =189a(11) =360a(12) =675a(13) =1304a(14) =2522a(15) =4835a(16) =9358a(17) =18193a(18) =35269a(19) =68568a(20) =133737a(21) =260802a(22) =509132a(23) =995801a(24) =1948931a(25) =3816904a(26) =7483636a(27) =14683721a(28) =28827798a(29) =56637969