a(n) is the number of binary strings of length n whose shortest run of 1s is of length 2.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =3a(5) =5a(6) =10a(7) =20a(8) =38a(9) =70a(10) =128a(11) =234a(12) =427a(13) =776a(14) =1404a(15) =2531a(16) =4550a(17) =8161a(18) =14608a(19) =26099a(20) =46550a(21) =82901a(22) =147441a(23) =261913a(24) =464759a(25) =823902a(26) =1459287a(27) =2582615a(28) =4567357a(29) =8072082