Number of length n binary words that have at least one maximal run of 1's having length two.

Terms

a(0) =0a(1) =1a(2) =2a(3) =5a(4) =11a(5) =25a(6) =55a(7) =120a(8) =258a(9) =550a(10) =1163a(11) =2444a(12) =5108a(13) =10627a(14) =22021a(15) =45474a(16) =93621a(17) =192232a(18) =393779a(19) =804947a(20) =1642355a(21) =3345307a(22) =6803734a(23) =13818636a(24) =28031472a(25) =56798821a(26) =114971348a(27) =232507076a(28) =469801235a(29) =948538807