Number of binary strings of length n that contain at least one maximal run of ones of even length.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =6a(5) =13a(6) =31a(7) =67a(8) =148a(9) =315a(10) =672a(11) =1410a(12) =2951a(13) =6123a(14) =12663a(15) =26054a(16) =53449a(17) =109278a(18) =222890a(19) =453533a(20) =921107a(21) =1867427a(22) =3780396a(23) =7642719a(24) =15433236a(25) =31132582a(26) =62744943a(27) =126354087a(28) =254265823a(29) =511337918