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

Terms

a(0) =0a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =43a(7) =91a(8) =191a(9) =398a(10) =824a(11) =1697a(12) =3480a(13) =7111a(14) =14487a(15) =29439a(16) =59694a(17) =120820a(18) =244153a(19) =492716a(20) =993171a(21) =1999923a(22) =4023679a(23) =8089182a(24) =16251760a(25) =32632321a(26) =65490672a(27) =131377999a(28) =263452079a(29) =528125695