a(n) is 2^n times the expected value of the shortest run of 0's in a binary word of length n.

Terms

a(0) =0a(1) =1a(2) =4a(3) =11a(4) =25a(5) =52a(6) =103a(7) =199a(8) =380a(9) =724a(10) =1382a(11) =2649a(12) =5103a(13) =9881a(14) =19224a(15) =37559a(16) =73646a(17) =144848a(18) =285623a(19) =564429a(20) =1117396a(21) =2215436a(22) =4398054a(23) =8740266a(24) =17385207a(25) =34607218a(26) =68934319a(27) =137386725a(28) =273942683a(29) =546450648