Number of binary strings of length n where the number of runs equals the number of 1s.

Terms

a(0) =1a(1) =1a(2) =0a(3) =2a(4) =4a(5) =5a(6) =12a(7) =25a(8) =42a(9) =83a(10) =168a(11) =312a(12) =600a(13) =1187a(14) =2284a(15) =4410a(16) =8644a(17) =16835a(18) =32736a(19) =64062a(20) =125340a(21) =244983a(22) =480020a(23) =941485a(24) =1846338a(25) =3624661a(26) =7122312a(27) =13999280a(28) =27532664a(29) =54185637