a(n) is the number of binary strings of length n whose shortest run of 1s is of length 3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =2a(5) =3a(6) =4a(7) =6a(8) =11a(9) =21a(10) =38a(11) =65a(12) =108a(13) =179a(14) =299a(15) =502a(16) =842a(17) =1406a(18) =2337a(19) =3872a(20) =6403a(21) =10575a(22) =17445a(23) =28742a(24) =47293a(25) =77720a(26) =127578a(27) =209210a(28) =342768a(29) =561131