Number of binary strings of length n with equal numbers of 0001 and 1000 substrings.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =26a(6) =50a(7) =100a(8) =200a(9) =400a(10) =800a(11) =1600a(12) =3200a(13) =6400a(14) =12800a(15) =25600a(16) =51200a(17) =102400a(18) =204800a(19) =409600a(20) =819200a(21) =1638400a(22) =3276800a(23) =6553600a(24) =13107200a(25) =26214400a(26) =52428800a(27) =104857600a(28) =209715200a(29) =419430400